WO2004084134A1 - Method for a sequential prediction of binary elements state in a binary process and the system for the method implementaion - Google Patents
Method for a sequential prediction of binary elements state in a binary process and the system for the method implementaion Download PDFInfo
- Publication number
- WO2004084134A1 WO2004084134A1 PCT/US2003/007857 US0307857W WO2004084134A1 WO 2004084134 A1 WO2004084134 A1 WO 2004084134A1 US 0307857 W US0307857 W US 0307857W WO 2004084134 A1 WO2004084134 A1 WO 2004084134A1
- Authority
- WO
- WIPO (PCT)
- Prior art keywords
- binary
- predicting
- resulting set
- prediction
- binary process
- Prior art date
Links
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N3/00—Computing arrangements based on biological models
- G06N3/12—Computing arrangements based on biological models using genetic models
- G06N3/126—Evolutionary algorithms, e.g. genetic algorithms or genetic programming
Definitions
- the present invention relates to methods and systems of prediction.
- the main object of the present invention is an extension of cognitive predicting methods on non-stationary processes.
- Every process can be viewed as a product of some entity's functioning. From that position, we may look at the process as the entity's output. We also may use the term object of prediction meaning the entity whose output shall be predicted. The binary process is frequently used for a representation of any other process that permits such mapping. All further descriptions will be done in view of the binary process prediction.
- the entity's properties are described in the form of various types of mathematical models such as sets of algebraic, differential, integral, stochastic equations, and their combinations.
- the predicting systems that employ the entity's model spans the wide range between the first attempts for extrapolation by Newton, Lagrange, etc. [G.A.Korn, 1961], and modern adaptive predictors [US Patent 5,424,942, 07/1995, 364#164, Dong,].
- the degree of complexity of prediction rises continuously.
- a Genetic Algorithm Representative Schema is a set of predicting solutions that are functions of the process ' argument . Every generation of such schema is a product of a multi-step optimization procedure that includes the Natural Selection Algorithm for an appropriate selection of the predicting solutions; Evolutionary Operators such as crossover, mutation, permutation, proportional reproduction, inversion, etc., for the new solutions generation; and a Fitness Function to be a measure of performance for each of those solutions;
- the representative schema optimization procedure acts on the specified interval of the binary process history to train the predicting system in recognizing the specifics of the process that is subjected to prediction; and • The predicting system produces a prediction of the forthcoming process element via calculating an output of the optimal predicting function at the next value of its argument.
- J. Koza A powerful extended genetic algorithm developed by J. Koza [US Patent 5,136,686, 08/1992] is good material for a discussion of strengths and weaknesses of the genetic algorithm approach in the context of non-stationary process prediction.
- the J. Koza's genetic algorithm is nonlinear. It not only includes the natural selection method and evolutionary operators, but also breaks down a problem into a hierarchy of subordinating sub-problems . This algorithm is free of the uniformity constraint that requires keeping the same size for all members of the population of predicting solutions.
- the J. Koza's genetic algorithm was not specifically designed for prediction. In the most general form given in the patent disclosure, this algorithm has the following description: "The process of the present invention operates upon a population of entities, which accomplish tasks and can vary in size and shape.
- Each iteration of the process comprises activating, selecting, choosing, performing, and adding.
- each entity activates to accomplish its goal and produces a result.
- a value is associated with the result of each activation and assigned to the corresponding entity.
- at least one entity having a relatively high associated value is selected.
- an operation is chosen from crossover, fitness proportionate reproduction, mutation, or permutation. If crossover is chosen, then the selected entity performs the crossover operation.
- Crossover creates new entities by combining portions of at least one selected entity with portions of at least one another entity.
- Fitness proportionate reproduction retains the selected entity in the population. Mutation randomly alters a small random part of an entity. Permutation reorders the parts of an entity without a net gain or loss.
- This procedure is used at the stage of genetic algorithm representative schema optimization. When the actual predicting procedure is active, it means that the forthcoming element of the binary process is really unknown.
- the discrete argument % of the binary process x( ⁇ ) is not necessarily a time variable.
- Each predicting function is made up of binary tokens, and may be considered as a chromosome;
- the predicting system initiates training until it finds the optimal predicting function pf 0 (X/ t q , t r ) , ⁇ e[t q ,t r ]; and,
- the fitness operator ⁇ of equation (1.2) may have a different view. However, each fitness function shares a common feature. Each fitness function in the predicting system provides an integral evaluation of the system's predicting ability. This evaluation is calculated on the interval [t q ,t r ] where (t r -t q )»l.
- the form of the fitness operator presented in expression (1.2) reflects the fact that the efficiency of prediction is higher as more correct predictions are produced with respect to the amount of incorrect predictions if both are observed on the same interval [t g ,t r ].
- the PFS - operator of equation (1.2) is responsible for changes in the population of pf - functions .
- This operator involves evolutionary operations to modify pf - functions from the previous iteration. It also produces a selection of those pf - functions which satisfy to the "good fit" selection condition.
- the "good fit" pf - functions are the source of new members in the PFj + i.
- the fitness function ⁇ ( ⁇ ) serves in this predicting algorithm as a measure of how successfully any pf - function returns predictions exclusively on the interval [t q ,t r ].
- the method described above possesses a distinctive peculiarity of genetic algorithms if viewed from the position of prediction. That is a utilization of the iterative optimization procedure for achieving the optimal predicting function.
- the optimization procedure is defined on certain interval of the binary process's "past" such that the search for the optimal predicting solution and the actual prediction are separated from each other.
- Adaptation is considered the ability of a system to modify its parameters and structure in response to changes to the system's environment.
- the role of the environment belongs to the object of prediction.
- the second property is an assumption about the existence of a representative set of solutions.
- a desired solution or solutions may be obtained by applying the Natural Selection Algorithm to the representative set of solutions .
- the third property is the idea that the existence of atomic elements (genes) combined to construct members (chromosomes) of the representative set of solutions (population of chromosomes) .
- the present invention solves the problem of sequential prediction of a binary element's state in a binary process.
- One object of the present invention is to provide a mathematical method and a computer algorithm to perform predictions of binary processes including non- stationary processes.
- a further object of the present invention is to provide the structure of the cognitive system for a sequential prediction of a binary element's state in a binary process that increases efficacy of functioning of any entity that includes this system as a subsystem.
- the present invention relates to methods and systems of prediction.
- the present invention provides the method for a sequential prediction of a binary element's state in a binary process and the system for the method embodiment.
- the binary processes are frequently used as a representation of a wide range of other processes that can be observed at outputs of various types of objects of prediction.
- the present invention is based on a representation of the chaotic nature as a "neighboring" order regularity whose separate parts preserve some order.
- the binary process was decomposed and specific atomic binary structures of minimal length were distinguished. A propagation of those structures in both directions of the binary process domain returns a stable, regular image. Such formations were denoted as the Elementary Behavioral Functions.
- dom[b k ( ⁇ , t , ⁇ k) ) ] [t k - ⁇ , t k ]
- ⁇ k is a period of the k-th elementary behavioral function
- dom[bk( ⁇ , t k , ⁇ k) ] is a domain of the function bk( ⁇ ,t k , ⁇ k ) [R- Elmasri and S. Navathe, 1994]. If taken with satisfaction to a condition of orthogonality, these functions become behavioral genes of the binary process, and constitute a genotype BG of the binary process ' behaviors .
- the present invention states that the genotype BG* is quasi-stationary relative to a character of change of two adherent elementary behavioral functions in expression (2.1) . Every binary process has its inherent behavioral genotype. In the case of a multi-dimensional system, each component x( ⁇ ) of a vectorial binary process x ( ⁇ ) has its inherent behavioral genotype.
- the process of prediction is recursive. It includes the following basic steps:
- the procedure is non-iterative and cyclic. Each cycle may contain several predictions .
- the PFk - set exists in various alternate versions.
- composition of this set is controlled by a function ⁇ ( ⁇ ) .
- This function is responsive to the current level of the binary process instability. It is fulfilled in the present invention that a cardinality of a set of predicting functions is inversely related to the evaluated instability level of the binary process, so that, for explicitly non- stationary processes the following statement is competent:
- the second stage is for prediction directly.
- the output of the prediction f ( ⁇ ) depends on prediction error's status of each PF k -set's member, current efficiency of prediction, and a set of binary indicators modifying a predicting algorithm.
- the retrospective prediction and the actual prediction both employ the Natural Selection Algorithm in a manner that each member of PF k participates in the current prediction cycle until this member produces an incorrect prediction.
- Each predicting function may again participate in prediction only in the next predicting cycle; and, 4. Updating the behavioral genotype membership and re- estimating the binary process instability level.
- the prediction method presented above is used in a predicting system that is the method's embodiment.
- the system is comprised of two subsystems - subsystem SSi, and subsystem SS 2 .
- the main objective of subsystem SSi is to determine a composition of the behavioral genotype set.
- Subsystem SSi provides these determinations on a periodical basis.
- Subsystem SSi is comprised of the following: a Binary Process Mapping Block (BM) , a Binary Process History Storage Block (H) , a Behavioral Genotype Creator (BG) , a Sampling Block (S) , and a Binary Process Shortest History Storage Block (HS) .
- the BM block quantifies, if necessary, the signal u(t) from an output of the object of prediction.
- the quantification may be performed by time and/or by level of the input signal.
- Every component of x( ⁇ ) is processed by a separate identical tract in SSi, and then the processed data from that tract come to a corresponding tract in SS 2 .
- a single component x( ⁇ )ex( ⁇ ) A block diagram of the one-dimensional predicting system is shown in Fig.6. The following conventions are present in the above illustration: SSi - Subsystem #1 SS - Subsystem #2
- V l , 2 , ... , n
- the H-block memorizes each sequential element of the process x( ⁇ ) that comes from the BM-block, and forms a binary string [x( ⁇ ) , t q , t p ] ⁇ h[x( ⁇ ) ] .
- the string h[x( ⁇ )] goes to an input of the BG-block and to an input of the HS-block.
- the latter creates a binary string hs [x( ⁇ ) , t ⁇ , t p ] ⁇ hs [x( ⁇ ) ] , s ⁇ q.
- the BG-block makes a decomposition (2.1) of the string h[x( ⁇ )] on the interval [t ⁇ r - ⁇ j) / t r ] , t r ⁇ t p .
- the ordering number j of the sample's length ⁇ is linked to the value t r when the decomposition has been initiated.
- the Sampling Block in the SSi-subsystern's local feedback controls the value of the ⁇ -j according to a criterion of statistical stability (e.g., the stability of the arithmetic average or both the arithmetic average and the standard deviation) of the biggest elementary behavioral function's period, taken from the sample.
- the ⁇ j ax variable defines a cardinal number of the BG—set.
- the BG - block generates members of the BG*j-set.
- the j-index in the behavioral genotype notation points to the fact that this set is going to be updated according to some schedule.
- the BG*-set's composition data is a main output of subsystem SSi- Information about the BG*-set membership comes to an input of each Selector of Predicting Functions of subsystem SS 2 .
- the binary string hs [x( ⁇ ) , t ⁇ , t p ] goes from an output of the HS-block to another input of the PFS-block of SS 2 .
- the BG-block receives a feedback signal from SS . This signal controls the schedule for updating the BG*-set.
- subsystem SS 2 The main objective of subsystem SS 2 is selecting the set of predicting functions from the BG*-set and then, performing a prediction.
- Subsystem SS 2 has some distinctive singularities :
- the subsystem involves a cyclic, non-iterative, and non-optimizing method of prediction
- the subsystem employs evaluation of the binary process instability. This evaluation is performed for selection of an appropriate set of predicting functions at the initial moment of a predicting cycle; and,
- Subsystem SS 2 is comprised of two contours .
- the first contour is the main contour of SS 2 .
- the PF k -set is an output of the PFS-block.
- the actual prediction f ( ⁇ ) is the first output of the P-block of the same contour.
- the second contour evaluates the binary process instability level.
- the second contour is comprised of several parallel channels. These channels have an identical structure such as PFSi -4 Pj -> Ej. Each channel generates a respective component of the estimating vector-function ⁇ ( ⁇ , t e , ⁇ e ) .
- the evaluation is performed by the application of the retrospective predicting procedure to some interval [t q ,t r ], t r ⁇ t p of the binary process history.
- t e is an evaluation schedule point
- ⁇ e (tq-t r ) denotes the length of the evaluation window.
- the second output of the P-block of the main contour is an indicator er( ⁇ ) of the error of prediction.
- This indicator signals to the exterior of SS 2 about the end of the current cycle of actual prediction.
- the BG-block of SSi takes into account the state of such "End-of-Cycle" indicator and uses this information for scheduling of the next update of the BG*-set.
- the er( ⁇ ) signal is also used by SS to perform the next instability evaluation of the binary process.
- a link between the P-block of SS 2 and the BG-block of SSi closes the global feedback in the predicting system.
- a human operator of the predicting system may update the schedules, as well as the setup parameters for the binary process decomposition and subsequent statistical analysis of the elementary behavioral f nctions .
- Predictions performed during a predicting cycle are independent of the evaluation procedure.
- Each of the three main procedures in the system the determination of the behavioral genotype, the evaluation of the binary process instability, or process' transients effect on predictability, and the selection of the set of predicting functions, which are active in the current predicting cycle) can be performed independently and do not affect the system' s speed.
- the prediction method described above increases the efficiency of the binary process prediction.
- This method extends the applicability of cognitive predicting systems in the field of non-stationary processes.
- the principal advantage of the method is a more intensive use of the most recent development in the binary process domain.
- the present invention does not demand to be in the zone [t p ,t p+w ], (w»l) of the guaranteed binary process stability.
- the iterative optimizing "Errors and Trials" genetic algorithm is not included in the predicting procedure of the present invention. This fact makes it possible for the application of the present invention to a population of real-time systems .
- the present invention can be incorporated in any system that permits mapping of at least one of the system's outputs on the space of binary processes.
- Fig.l depicts a block diagram of a modern predicting system based on the genetic algorithm approach
- Fig.2 is a generalized algorithm of a method for a sequential prediction of a binary element's state in a binary process
- Fig.4 presents examples of Embodiment 1 and Embodiment 2 of a predicting algorithm of the present invention
- Fig.5 is an illustration of a binary process mapping on the space of binary processes
- Fig.6 depicts the block diagram of a predicting system for a sequential prediction of a binary element's state in a binary process
- Fig.7 depicts an original measuring system block diagram
- Fig.8 depicts a block diagram of a measuring system with a signal-to-noise ratio prediction
- Fig.9 illustrates a measurement with a signal-to-noise ratio prediction
- Fig.10 illustrates the compensation of a measuring system's filter saturation by means of prediction
- Fig.11 depicts a fragment of the output of a three-point moving average function of a time series SPREAD
- Fig.12 illustrates a mapping of the econometric time series SPREAD on the space of binary processes
- Fig.13 illustrates a prediction of the econometric time series SPREAD elements .
- the present invention describes a method for a sequential prediction of a binary element's state in a binary process and a system for this method embodiment.
- numerous specific details are set forth in order to prove a thorough understanding of the present invention. Mathematical notation is frequently used to keep the description as accurate as possible. It will be obvious, however, to one skilled in the art that the present invention may be practiced without using these specific details. In other instances, well-known methods, structures, and representations have not been described in detail so as not to unnecessarily obscure the present invention.
- the generalized algorithm of the new method of prediction of a binary process element's state is shown in Fig.2. The following conventions are present in the above illustration:
- Block 1 Begin
- Block 4 Evaluation of the binary process instability Level or process ' transients effect on predictability
- Block 6 Updating the behavioral genotype membership and re-estimating of the binary process instability level
- Block 7 Block 8: Output
- the method of prediction is recursive. It includes the following basic steps that must be fulfilled for every single binary process or for each component of a vectorial binary process :
- the corner stone of the present invention is the concept of a binary process behavioral genotype .
- a definition of the behavioral genotype is based on a representation of the chaotic nature in the form of a "neighboring order" regularity whose separate parts preserve some order. This assumption allows a decomposition of the binary process into specific atomic binary structures of a minimal length. A propagation of those structures in both directions of the binary process' discrete argument domain returns a stable, regular order.
- ⁇ k is the elementary behavioral function's period; dom[b ( ⁇ , t k , ⁇ k ) ] is a domain of the function b k ( ⁇ ,t k , ⁇ k ) [R. Elmasri and S. Navathe, 1994]. If taken with satisfaction to an orthogonality condition, these functions become behavioral genes of the binary process and constitute a genotype BG of the binary process ' behaviors :
- a behavioral gene of the BG - set is a binary periodical function of a discrete argument ⁇ .
- ⁇ i is a period of the i-th gene, and 5 is its current phase;
- ⁇ max (t r , ⁇ ) is the biggest statistically stable period among the periods of the elementary behavioral functions.
- the ⁇ max (t r , ⁇ ) serves as a parameter of the set BG.
- the ⁇ max (t r , ⁇ ) is determined as a result of statistical analysis performed on the binary process decomposition (3.1) . This decomposition is defined on a representative interval [t q ,t r ], ( ⁇ »l) . Every binary process has its inherent behavioral genotype. In the case of a multi-dimensional system, each component of a vectorial binary process has its inherent behavioral genotype.
- P ⁇ x(ti) ,x(t ⁇ + ⁇ ) ⁇ is a probability of the existence of two particular sequential elements x(ti) , x(t ⁇ + ⁇ ) in the binary process x( ⁇ ) .
- a normal form for a behavioral gene is when the positive part is observed first.
- the gene's current phase 05 is the amount of elements counted on the interval between its first positive element and the element that corresponds to the value of the gene's argument designated as a point of observation (t*) .
- He(z) is the Heaviside's Step Function
- Int(z) is the Integer Function of the real argument zeR
- Each member of the C-set has the same range as the members of the BG-set.
- the BG-set identification can be either a stage of the predicting system design, or can be included in an algorithm of the automated predicting system.
- model (1.2) in the present invention is used for the binary process instability evaluation. That procedure is incorporated in the evaluating function ⁇ ( ⁇ , t q , t r ,PF) ⁇ ( ⁇ ) .
- This function directly provides the quantitative information about the efficiency of prediction performed on the interval [t q ,t r ], t r ⁇ t p .
- the evaluating function's output depends on the composition of the PF-set that is directly involved in prediction. Therefore, the function ⁇ ( ⁇ ) measures how unstable the binary process was if observed before the cycle of actual predictions .
- ⁇ ⁇ ( ⁇ ) ⁇ ( ⁇ ,t e , ⁇ e ) , ⁇ 2 ( ⁇ , t e , ⁇ e ) ,..., ⁇ n ( ⁇ ,te, ⁇ e ) ⁇ (3.6)
- t e is an evaluation schedule point
- parameters t e , and ⁇ e may have different values for each component of the vector-function ⁇ ( ⁇ ) .
- a determination of the ⁇ -vector's composition is a system design task. The formulas presented below, are the embodiments the authors of the present invention have used for the implementation of the method:
- each component of the ⁇ -vector is obtained by applying a non-iterative retrospective predicting procedure F(PF, ⁇ ).
- F(PF, ⁇ ) the retrospective predicting procedure's algorithm does not substantially differ from the algorithm for the actual predicting procedure.
- the difference between these algorithms includes two points. The first point is the value of the argument ⁇ of the process x( ⁇ ) at the beginning moment of the prediction.
- the second point is the retrospective predicting procedure (serving the binary process stability evaluation) employs an assignment of the PF-set's composition at the beginning of each predicting cycle.
- the actual predicting procedure employs a selection of the PF- set's composition at the beginning of each predicting cycle.
- One component of the ⁇ (x) may also be estimating function (3.7) where the PF- set is a singleton ⁇ pf op t (x. t q , t r ) ⁇ .
- the PF-set might be a product of prior art system (1.2) .
- the predicting method of the present invention can be implemented without the involvement of the binary process instability evaluation. In that case, a designer must be aware of the expected degree of binary.process instability or non-stationarity. Therefore, the initial composition of the PF-set in the cycle of the actual predicting procedures must be predetermined.
- ti is the beginning point of performing the prediction
- t p is the latest observed value of the binary process discrete argument.
- the PF k -set exists in multiple alternate versions, so that PF k cPFS(BG*j) .
- the composition of the PF k -set is controlled by a function ⁇ ( ⁇ k ) . This function is responsible for analysis of the current stability evaluation data. The selection law is as follows
- the MAX - function here is the relational algebra aggregate function returning a maximum value from a sequence of values [R. Elmasri and S. Navathe, 1994].
- the proposed selection law allows a predetermination of the set PF by requiring ⁇ k ,i> ⁇ °.
- the following rule controls the PF-set selection if the process x(t) is explicitly non-stationary:
- Vpfi( ⁇ ,G5i, ⁇ i)ePF (3.12)
- Vl (l,2,...,I k )
- Property expression (3.11) points at the fact that each predicting function used for a non-stationary process prediction belongs to this process' behavioral genotype.
- the specific part of the PF-set selection condition depends on the peculiarities of the object of prediction. A determination of this specific part is a system design task. The authors of the present invention have found effective the following embodiments of the specific part of the PF-set selection condition for non-stationary binary processes:
- the PF-set includes each element gi of the BG*-set that can be selected on the binary process historical interval ⁇ and:
- a predicting function is called, respectively, the Pair Predicting Function, or the- Triple Predicting Function.
- Embodiment 2 is a diagrammatic representation of Embodiment 1 :
- the PF-set includes each element gi of the BG*-set that can be selected on the binary process historical interval ⁇ and:
- each predicting function characterized by a corresponding identified sequence parameter ⁇ or ⁇ belong to the PF-set.
- the second stage is for prediction directly.
- the prediction f (ti + i) of the k h predicting cycle is returned by the operator F acting upon the set PF k of predicting functions such that:
- Expression (3.13) includes a model x' (ti+i) of a state of the binary process' forthcoming element, and it also includes a binary indicator y(t ⁇ + ⁇ ) that permits the prediction.
- the expression (3.14) reveals a structure of the model x' (ti + i) .
- the model x' (t p+ ⁇ ) of the binary process' forthcoming element employs the Natural Selection Algorithm in the way that each member of PFk participates in the current prediction cycle until this member produces an incorrect prediction.
- the model x' (ti + i) is a product of a nonlinear transformation of a fundamental model x°(ti + ⁇ ), so that
- the prediction f (ti + i) can be halted or the fundamental model ' s output can be inverted depending on the values of ⁇ (t p + ⁇ ) , ⁇ (t p+ ⁇ ) , and ef(t p ).
- the complete mathematical description of the second stage of the predicting algorithm is presented below in the form of recurrent operator equations of Boolean variables.
- Each PF k -set member is also shown beginning with the sequence's eighth element. This drawing makes a clear vision of the mechanism of prediction. Prediction is not allowed until a conjunction of the predicting functions has released the prediction. Then, the Natural Selection Algorithm is applied to the PF k -set.
- the function pf ⁇ [ ⁇ , ⁇ ] ⁇ (lpln) which is the winner in the first cycle of prediction, becomes the outsider in the next cycle.
- the leader in the second cycle is pfi 5 [ ⁇ , ⁇ i 5 ] ⁇ (5pln) .
- Each member of the PF-set has its own initial phase 05 (t c ) that is calculated at the beginning moment of the predicting cycle.
- the behavioral genotype (BG*) itself can not be used as the set of predicting functions in many cases with non- stationary binary processes.
- the replacement of identical functions b 3 , b 4 as well as the replacement of function be, which is almost identical to b 5 makes the selection for this example, BG*- set, inapplicable for a prediction.
- the PF-set having an abundant number of members causes a frequent blocking of the prediction with an absence of correct predictions in the predicting cycle.
- neglecting most of the elements in the composition of the behavioral genotype leads to an increase in the number of prediction errors with simultaneous contraction of the predicting cycle.
- the first stage of the predicting algorithm designed for the determination of the PF-set' s composition at the initial point of the predicting cycle is of great importance.
- a convincing example of applying Embodiment 1 and Embodiment 2 to the prediction of the sequence of a binary game random outcome is depicted in Fig.4.
- the following conventions are present in the above illustration: inv. - inversion predicting mode and dir. - direct predicting mode.
- the end-point of a k th current predicting cycle and the beginning-point of the next predicting cycle is the same point.
- two actions might be taken.
- the first action is a re-estimating of the binary process instability level .
- the second action is a recalculating of the BG-set membership. Both actions are subordinate to some schedule.
- the schedule is a part of the method's implementation algorithm.
- the same algorithm re-estimates the binary process instability level accordingly with a schedule that is functionally dependent on the beginning of a predicting cycle.
- the particular schedule selection depends on the object of prediction and may be determined during the method's implementing system design or to be a product of an adaptive scheduling subsystem incorporated in such an implementing system.
- the method of prediction described above increases the efficacy of the binary process prediction.
- This method expands the applicability of cognitive predicting systems in the field of non-stationary processes.
- the principal advantage of the method is a more intensive use of the most recent developments in the binary process domain.
- the present invention does not demand to be in the zone [t p/ t p+w ], (w»l) of the guaranteed binary process stability.
- the iterative optimizing "Errors and
- Trials genetic algorithm is not included in the predicting procedure of the present invention. This fact makes it possible for the application of the present invention to a population of real - time systems.
- the present invention can be incorporated in any system that permits mapping of at least one of the system's outputs on the space of binary processes.
- the predicting system has a two level hierarchy.
- the first level is a subsystem (SSi) for the behavioral genotype identification.
- the second level is a subsystem (SS 2 ) for the sequential prediction of a binary element's state in the binary process.
- the global input of the predicting system is an output of the object of prediction.
- the real object of prediction may have a continuous output. Let this output be denoted as u(t)eU.
- the binary process x( ⁇ )eX is a result of a mapping of the set U of continuous functions into the set X of discrete binary functions.
- the BM-block quantifies, if necessary, the signal u(t). The quantification may be performed through a time sampling procedure and/or an amplitude qualification.
- the value u° is a single quantizing level.
- each component of the vector x( ⁇ ) is a product of this two-step (3.31, 3.32) procedure.
- B ⁇ B( ⁇ ,u°) u(t) ⁇ x(x) .
- the parameter ⁇ defines the sampling rate of the quantification.
- Subsystem SSi The main objective of subsystem SSi is to determine a composition of the behavioral genotype set. The SSi-subsystem provides such determination on a periodical basis.
- Subsystem SSi is comprised of a Binary Process Mapping Block (BM) , a Binary Process History Storage Block (H) , a Behavioral Genotype Creator (BG) , a Sampling Block (S) , and a Binary Process Shortest History Storage Block (HS).
- BM Binary Process Mapping Block
- H Binary Process History Storage Block
- BG Behavioral Genotype Creator
- S Sampling Block
- HS Binary Process Shortest History Storage Block
- the H-block memorizes the state of each sequential element of the process x(x) that comes from the BM-block, and forms a binary string h[x( ⁇ ) , t q , t p ] ⁇ h[x( ⁇ ) ] .
- the storage space of the H-block depends on the object of prediction's peculiarities and must be determined during the system design.
- the string h[x( ⁇ ) ] goes to an input of the BG-block and to an input of the HS-block. The latter creates a binary string hs [x( ⁇ ) , t s , t p ] ⁇ hs [x( ⁇ ) ] , s ⁇ q.
- the BG-block makes a decomposition expression (3.1) of the string h[x( ⁇ )] on the interval [t( r _ ⁇ ) , t r ] , t r ⁇ t p .
- the ordering number j of the sample's length ⁇ j is linked to the value t r when the decomposition has been initiated.
- the Sampler in subsystem SSi local feedback controls the value of ⁇ j according to a criterion of robustness, (e.g., the stability of the sample mean, or both the mean and the standard deviation) of the biggest elementary behavioral function's period ⁇ max (t r , ⁇ j ) ⁇ j max taken from the sample.
- the ⁇ j max variable is a substantial parameter of the predicting system. It follows from expression (3.4), that T
- the BG-block generates members of the BG*j-set by formulas (3.4), (3.5).
- the j- index in the behavioral genotype notation points to the fact that this set is going to be updated according to some schedule.
- the BG*j-set's composition data is a main output of subsystem SSi. Information about the BG*j-set's membership comes to the inputs of each Selector of the Predicting Functions of subsystem SS 2 .
- the binary string hs [x( ⁇ ) , t s , t p ] goes from an output of the HS-block to another input of the PFS-block of SS 2 .
- the BG-block receives a feedback signal from SS 2 - This signal controls the updating schedule for the BG*-set.
- Subsystem SS 2 The main objective of subsystem SS 2 is selecting the set of predicting functions from the BG*-set and then, performing a prediction. Subsystem SS 2 has some distinctive singularities :
- the subsystem involves a cyclic, non-iterative, and non-optimizing method of prediction.
- the subsystem employs the binary process instability evaluation for a selection of an appropriate set of predicting functions at the initial moment of a predicting cycle.
- the evaluation may, but not necessarily involve traditional genetic algorithm schemes .
- the subsystem insures that the cardinality of the set of predicting functions is inversely related to the evaluated binary process instability level, or_transient effects on predictability, so that, for the explicitly non- stationary processes PF k - ⁇ BG*j .
- Subsystem SS 2 is comprised of two contours.
- the first contour is the main contour of SS 2 .
- the PF k -set is an output of the PFS-block.
- the actual prediction f ( ⁇ ) is the first output of the P-block of the main contour.
- the second contour evaluates the binary process instability level.
- the second contour is comprised of several parallel channels . These channels have an identical structure such as PFSi — Pi — Ei. Each channel generates a respective component of the estimating vector-function ⁇ ( ⁇ ,t e ), which is defined by expressions (3.6)-(3.8). Evaluation is performed by application of the retrospective predicting procedure to some interval [t q ,t r ], t r ⁇ t p of the binary process history.
- t e is an evaluation schedule point.
- the second output of the P-block of the main contour is the indicator er( ⁇ ) defined by expression (3.20).
- This indicator signals to the exterior of subsystem SS 2 about the end of the current cycle of actual prediction.
- the BG-block of the subsystem SSi takes into account the state of such "End-of-Cycle" indicators and uses this information for scheduling of the next update of the BG*-set.
- the er( ⁇ ) signal is also used by SS 2 to perform the next instability evaluation of the binary process .
- a link between the P-block of the SS-subsystem and the BG-block of the SSi-subsystem closes the global feedback in the predicting system.
- a human operator of the predicting system may update the schedules, as well as the setup parameters for the binary process decomposition and subsequent statistical analysis of the elementary behavioral functions.
- the possibility of the human operator's involvement is reflected in the block diagram of the predicting system as the second input of the BG-block in SSi-subsystem and as the first input of the PFS-block in SS 2 - subsystem.
- Predictions performed during a predicting cycle are independent of the evaluation procedure.
- Each of the three main procedures in the system the determination of the behavioral genotype, the evaluation of the binary process instability, and the selection of the set of predicting functions, which are active in the current predicting cycle) can be performed independently and do not affect the system's speed.
- the method allows performing real time predictions of binary processes, including non-stationary processes, regardless of possible speed and memory limitations of computing resources.
- the predicting system that implements the method increases efficiency of any entity that includes this system as a subsystem.
- u(t) is an unknown useful signal that reflects the value ⁇ (t) .
- the signal y(t) is an additive noise.
- the vector of the filter's parameters consists of a gain factor Kf and a vector T f of time-dimensional constants characterizing the filter's dynamics, so that The remaining part of the system might be described in general by a nonlinear operator Q[D, ⁇ , s f (t) ] , D ⁇ d/dt.
- a multiplicative disturbance also might exist in the system.
- the low p(t) indicates that the system is unable to produce an accurate measurement.
- a traditional approach for the noise rejection is filtration. However, no filter of any kind can produce a total noise rejection. Thus, the system's filtering ability bounds the accuracy and the precision of the measurement.
- the present invention provides a new powerful solution for a problem of additive noise rejection and for a problem of multiplicative disturbances compensation in measuring systems. The new approach works well in those cases where the traditional methods fail.
- the solution is based on a measuring algorithm that returns each resulting measurement Vj ⁇ v(tj, ⁇ j) by an aggregation of a string of controllable sub-measurements.
- the tj is the j th moment of the discrete time when the resulting measurement is done; the ⁇ j indicates the length of such measurement.
- the sub-measurement ⁇ j,i ⁇ (tj,i, ⁇ j, ⁇ ) of the measurement v(tj, ⁇ j) is a specifically selected output of a measuring block-procedure.
- the measuring block-procedure ⁇ ,is ⁇ (t,i, ⁇ , ⁇ ) is a completed measurement associated with an index number (i) of each repetition of the measuring algorithm.
- the evaluation formula is similar to formula (3.32) where u(t) and u°(t) are substituted respectively with p(t) and p°.
- the j th outcome measurement v(tj, ⁇ j) needs to be organized as an aggregate function A of a sequence of those sub-measurements, i.e.,
- the measuring block-procedure ⁇ j, ⁇ is executed regularly at each moment tj,i and does not depend on the process x( ⁇ ) .
- Parameter ⁇ j,i is the duration of the procedure ⁇ (tj,i, ⁇ j, ⁇ ) .
- the sub-measurement Vj, ⁇ accepts a value of the measuring block-procedure ⁇ j,i only if such action is permitted by control function %j,i ⁇ % .t-j.i) .
- the measuring block-procedure may have a rather complex algorithm. However, it follows expression (3.35), that an interval between two adjacent measurements (V , Vj +i ) is defined by a sum of the duration of each measuring block- procedure that is involved in the current measurement. Number m of such procedures can be predetermined or can be calculated by the system itself based on a criterion of a desired accuracy, and so forth. The same approach is used for the multiplicative disturbance rejection. Once the prediction of the signal-to-noise ratio has indicated “low", the measuring system automatically switches to a multiplicative disturbance compensation mode. Information about measured value ⁇ (t) is locked in " this mode. A testing noiseless signal goes to the system's input instead of signal s(t). This signal is used for the adjustment of the system's drifting parameters. Thus, the measuring system with the signal-to-noise ratio prediction mostly accumulates data with a low noise component.
- the system is comprised of a Measuring Block-Procedure Subsystem (MBP) , an Aggregation Block (AGB) , a Signal-to- Noise Ratio Predictor (P) , and a Measuring Process Control Block (MCB) .
- MBP Measuring Block-Procedure Subsystem
- AGB Aggregation Block
- P Signal-to- Noise Ratio Predictor
- MB Measuring Process Control Block
- the input of subsystem MBP is either informative signal s(t) (if the system. orks in the measuring mode), or testing noiseless signal u st (t) (if the system works in the adjustment mode) .
- Another output of subsystem MBP is binary process x(T) or binary vector- process x( ⁇ ) , which is the binary evaluation of the signal- to-noise ratio.
- Signal x( ⁇ ) goes to an input of the predictor.
- Predictor P generates a prediction f ( ⁇ ) of element x( ⁇ ) corresponding to a forthcoming result ⁇ ( ⁇ ) of the measuring block-procedure.
- the MCB-block produces output signal ⁇ (t) that simultaneously controls sub-measurement's value ⁇ ( ⁇ ) . If the forecasted level of the p( ⁇ ) is high, the sub-measurement ⁇ ( ⁇ ) has some value and is accounted in the j th measurement Vj . If the forecasted level of p( ⁇ ) is low, sub-measurement ⁇ (t) is not accounted in the j th measurement Vj.
- the static accuracy (A) of the measuring system may be evaluated as follows:
- Signal s(t) and S f (t) in expression (3.38) are accessible.
- Signal p(t) can also be obtained by measuring the noise component involving a separate channel of MBP. In that case, the noiseless testing signal is employed, and a correlation between the actual noise y(t) and the noise measured at the separate channel must be proved.
- er( ⁇ ) is the prediction method's error described in expression (3.20).
- Discrete time ⁇ characterizes sub- measurements of the j th measurement.
- Expression (3.46) shows that by having the effective predictor in the measuring system, the possible low noise component in the current measurement, is ⁇ times greater than the possible high noise component, ⁇ >1. The approach explained above was proven experimentally.
- the sample of digital output of an ultrasonic distance meter was used in a computer simulation of the predictor.
- the receiving stage of such a system is comprised of a preamplifier and a filter.
- the mathematical model of these devices may contain the following expressions :
- value V is the filter's power supply voltage
- value K a is the preamplifier's amplification factor.
- the method of the present invention can be employed for a prediction of the moment of the possible filter's saturation. Then, the sub-measurement containing saturated filter would not be accounted for in the current measurement similar to what was presented in expressions (3.33) - (3.35). To get that algorithm suitable to the current problem, the multiple-level quantification should be involved.
- process x 3 ( ⁇ ) of the lower quantizing level s ax ⁇ ) can be used for the prediction.
- the elementary behavioral functions of process x 3 ( ⁇ ) encircle the moment of saturation observed in binary process 4 ( ⁇ ). Therefore, to work out the effect of substantial non-linearity, we need to use a multidimensional predicting algorithm has to be invoked.
- the art of design is the establishment of the sufficient amount of quantizing levels in such a measuring system.
- a multiplicative disturbance can be rejected by switching the system's input from signal s(t) to a testing signal in order to adjust the system's unstable parameters. This switching has to be accomplished at the moment of prediction of the filter's saturation.
- the multi-dimensional version of the present invention can be used in econometrics known as the time series analysis.
- Let there be a time series which is a 3-point moving average of the difference between the stock price "High” and the stock price “Low” . These variables are very popular in the field of stock market.
- the procedure B( ⁇ ,u°) of expressions (3.31 and 3.32) should be applied.
- the time series Spread is already defined on the discrete time domain, i.e., the sampling rate ⁇ is predetermined.
- the process Spread( ⁇ ) ⁇ u. ( ⁇ ) >0 of the present example has the following mapping on the vector x( ⁇ ) :
- the object of the econometric analysis is to determine whether or not the particular time series belongs to some interval on its range. Define each quantizing level of (3.48) as such interval's upper/lower bound so that:
- every process u( ⁇ ) is linked to two binary processes Xj ( ⁇ ) and Xj+ ⁇ ( ⁇ ) according to statement (3.50).
- a forthcoming element of a binary process j ( ⁇ ) will be "+”can not be determined with sufficient predictability.
- the predicting method's efficiency evaluation (3.7), it means that ⁇ j (t/ t q , t r ) ⁇ * , ⁇ *>l.
- the predictability of the fact that the next element of the same process XJ ( ⁇ ) will be "-" is much greater than ⁇ * .
- the ⁇ Locating Condition> is the following selection condition:
- evaluation function ⁇ [R l ( ⁇ , t q , t r ) ,W l ( ⁇ , t q , t r ) ] is defined by formula (3.7) .
- a data acquisition system which is basically comprised of several sources of data, transmitters that deliver data over some media or through an interface, receivers, and signal/data processing devices.
- Each informative channel experiences some interference existing in the form of additive and/or multiplicative disturbance.
- one or more channels demonstrate a lesser level of disturbance in comparison with other channels of the system if observed at any moment in time.
- a prediction of the next channel free of disturbance can be performed by the method of the present invention.
- the approaches presented in the description of Application 1 and Application 2 are useful in accomplishing this objective.
- the data processing device may be switched to receive information that will be coming through the less disturbed informative channel .
- the method of the present invention allows a simplification of the error correction algorithms, and increases the memory capacity and the system's speed.
- the cases that correspond with this application relate to those categories where the content of a message carries priority over the moment when the communication takes place.
- An example could be a communication under a disaster condition.
- the content of the message is vitally important, and the value of time spent for the setup of communication arrangement has a survival meaning as well.
- Another example could be a problem of a remote control of an object (a space ship, a nuclear power station, a chemical plant, etc.) with random failures.
- Providing a high quality cellular phone communication is also that kind of problem.
- the predicting method of the present invention is a possible solution for the problems listed above.
- the following sketch-algorithm is an illustration of how the method of a binary process prediction can be used for improving the quality of the cellular phone conversation. This is accomplished by predicting and subsequently advising the user about the moment of best physical conditions of communications. Assume that there is a cellular phone network where each user is linked to the host station:
- Each telephone automatically responds to a time scheduled check-signal on the reserve frequency generated by the station.
- the responses are binary-classified by the good communication quality criterion and the users are respectively separated into two groups. Then, the forthcoming membership for both groups is predicted.
- a user may expect to receive an appropriate notifying message when attempting to contact any member of the "bad communication quality group" .
- a continuous check - response dialog takes place between the host station and each communicator. This dialog is accompanied by the communication quality prediction. If a failure of some communication is predicted, then both participants may receive the notifying message.
- the present invention may be viewed as a computer- based game's algorithm where the human intelligence and the artificial intelligence compete.
- a human-player generates a binary string of elements of a finite length where a computer program must predict the forthcoming element ' s state. The number of correct and incorrect predictions is evaluated on at least one binary string length so that the human wins and respectively the artificial mind loses if some predetermined threshold is exceeded by the evaluation.
- a set of such evaluating thresholds and the predicting algorithm's internal parameters can be established by a human player to set a game to different levels of complexity. Thus, a different result in this game is expected depending on how skilled the human player is.
Abstract
Description
Claims
Priority Applications (3)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
PCT/US2003/007857 WO2004084134A1 (en) | 2003-03-14 | 2003-03-14 | Method for a sequential prediction of binary elements state in a binary process and the system for the method implementaion |
EP03716569A EP1609118A1 (en) | 2003-03-14 | 2003-03-14 | Method for a sequential prediction of binary elements state in a binary process and the system for the method implementaion |
AU2003220271A AU2003220271A1 (en) | 2003-03-14 | 2003-03-14 | Method for a sequential prediction of binary elements state in a binary process and the system for the method implementaion |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
PCT/US2003/007857 WO2004084134A1 (en) | 2003-03-14 | 2003-03-14 | Method for a sequential prediction of binary elements state in a binary process and the system for the method implementaion |
Publications (1)
Publication Number | Publication Date |
---|---|
WO2004084134A1 true WO2004084134A1 (en) | 2004-09-30 |
Family
ID=33029244
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
PCT/US2003/007857 WO2004084134A1 (en) | 2003-03-14 | 2003-03-14 | Method for a sequential prediction of binary elements state in a binary process and the system for the method implementaion |
Country Status (3)
Country | Link |
---|---|
EP (1) | EP1609118A1 (en) |
AU (1) | AU2003220271A1 (en) |
WO (1) | WO2004084134A1 (en) |
Citations (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US5991340A (en) * | 1996-06-25 | 1999-11-23 | Seiko Epson Corporation | Method and system for encoding and decoding data using run prediction |
US6055273A (en) * | 1996-09-02 | 2000-04-25 | Seiko Epson Corporation | Data encoding and decoding method and device of a multiple-valued information source |
US6581047B1 (en) * | 1999-04-07 | 2003-06-17 | Inesa, Inc. | Method for a sequential prediction of binary element's state in a binary process and the system for the method implementation |
-
2003
- 2003-03-14 AU AU2003220271A patent/AU2003220271A1/en not_active Abandoned
- 2003-03-14 WO PCT/US2003/007857 patent/WO2004084134A1/en not_active Application Discontinuation
- 2003-03-14 EP EP03716569A patent/EP1609118A1/en not_active Withdrawn
Patent Citations (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US5991340A (en) * | 1996-06-25 | 1999-11-23 | Seiko Epson Corporation | Method and system for encoding and decoding data using run prediction |
US6055273A (en) * | 1996-09-02 | 2000-04-25 | Seiko Epson Corporation | Data encoding and decoding method and device of a multiple-valued information source |
US6581047B1 (en) * | 1999-04-07 | 2003-06-17 | Inesa, Inc. | Method for a sequential prediction of binary element's state in a binary process and the system for the method implementation |
Also Published As
Publication number | Publication date |
---|---|
EP1609118A1 (en) | 2005-12-28 |
AU2003220271A1 (en) | 2004-10-11 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
CN110490717B (en) | Commodity recommendation method and system based on user session and graph convolution neural network | |
Palacios et al. | Genetic tabu search for the fuzzy flexible job shop problem | |
Paliwal et al. | Reinforced genetic algorithm learning for optimizing computation graphs | |
Västberg et al. | A dynamic discrete choice activity-based travel demand model | |
Gero et al. | An exploration‐based evolutionary model of a generative design process | |
Freyman et al. | Application of fuzzy logic for decoding and evaluation of results within the process of information system components diagnosis | |
Yamada et al. | Feature-selection based data prioritization in mobile traffic prediction using machine learning | |
Tang et al. | Dynamic games among teams with delayed intra-team information sharing | |
He et al. | Cooperative-competitive reinforcement learning with history-dependent rewards | |
US6581047B1 (en) | Method for a sequential prediction of binary element's state in a binary process and the system for the method implementation | |
Ozbay et al. | Modeling route choice behavior with stochastic learning automata | |
Li et al. | Rate-optimal contextual online matching bandit | |
Gosavi | Solving Markov decision processes via simulation | |
CN111832817A (en) | Small world echo state network time sequence prediction method based on MCP penalty function | |
González-Rodríguez et al. | A genetic solution based on lexicographical goal programming for a multiobjective job shop with uncertainty | |
WO2004084134A1 (en) | Method for a sequential prediction of binary elements state in a binary process and the system for the method implementaion | |
Dursun et al. | Data pooling for multiple single-component systems under population heterogeneity | |
Kumar et al. | Transfer Learning based GDP Prediction from Uncertain Carbon Emission Data | |
Crone et al. | Feature selection of autoregressive neural network inputs for trend time series forecasting | |
Wall | Emergence of coordination in growing decision-making organizations: The role of complexity, search strategy, and cost of effort | |
AbAziz et al. | Voltage stability prediction by using artificial immune least square support vector machines (AILSVM) | |
Ratitch | On characteristics of Markov decision processes and reinforcement learning in large domains | |
Lücke et al. | Learning interpretable collective variables for spreading processes on networks | |
CN112383965B (en) | Cognitive radio power distribution method based on DRQN and multi-sensor model | |
Bashir et al. | Adaptive-Greedy Exploration for Finite Systems |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
AK | Designated states |
Kind code of ref document: A1 Designated state(s): AE AG AL AM AT AU AZ BA BB BG BR BY BZ CA CH CN CO CR CU CZ DE DK DM DZ EC EE ES FI GB GD GE GH GM HR HU ID IL IN IS JP KE KG KP KR KZ LC LK LR LS LT LU LV MA MD MG MK MN MW MX MZ NI NO NZ OM PH PL PT RO RU SC SD SE SG SK SL TJ TM TN TR TT TZ UA UG UZ VC VN YU ZA ZM ZW |
|
AL | Designated countries for regional patents |
Kind code of ref document: A1 Designated state(s): GH GM KE LS MW MZ SD SL SZ TZ UG ZM ZW AM AZ BY KG KZ MD RU TJ TM AT BE BG CH CY CZ DE DK EE ES FI FR GB GR HU IE IT LU MC NL PT RO SE SI SK TR BF BJ CF CG CI CM GA GN GQ GW ML MR NE SN TD TG |
|
121 | Ep: the epo has been informed by wipo that ep was designated in this application | ||
WWE | Wipo information: entry into national phase |
Ref document number: 2003716569 Country of ref document: EP |
|
WWP | Wipo information: published in national office |
Ref document number: 2003716569 Country of ref document: EP |
|
NENP | Non-entry into the national phase |
Ref country code: JP |
|
WWW | Wipo information: withdrawn in national office |
Country of ref document: JP |