JP2010257269A - Probabilistic inference device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a probabilistic inference device for quickly and efficiently performing inference processing by using a Bayesian network having a mechanism for restricting the combination of the values of nodes representing random variables. <P>SOLUTION: The probabilistic inference device includes an inference mechanism for performing inference processing by using a Bayesian network configuring a network by a plurality of node representing random variables and edges representing causality between the random variables between the nodes, wherein constraints are added to the combination of the values of the Bayesian network in order to reduce the degree of freedom of the combination of the values. As a technological means for constraining the values, a method for adding constraint nodes to the Bayesian network is used. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to a probabilistic inference apparatus using a Bayesian network knowledge representation technique, and more specifically, infers using a Bayesian network having a mechanism that limits combinations of possible values of nodes representing random variables. The present invention relates to a stochastic reasoning apparatus that performs processing at high speed and efficiency.

  A Bayesian network (Non-Patent Document 1) is a data structure for storing a stochastic causal relationship between a plurality of random variables on a memory of a computer. By using the Bayesian network, complex knowledge can be efficiently expressed, and various probabilistic inferences such as posterior probability calculation and MPE calculation can be performed based on the knowledge. Currently, Bayesian networks have a wide range of applications, such as pattern recognition for voice and images, robot motion control, natural language processing, and knowledge information processing. A hidden Markov model (HMM) often used in speech recognition is a type of Bayesian network.

  A Bayesian network is composed of a network of a plurality of nodes, with nodes representing random variables and edges representing causal relationships between random variables between the nodes. Furthermore, what is called a conditional probability table is held for each node. The conditional probability table is a table of conditional probabilities that take a certain value when a set of parent values of a node takes a certain value combination.

  FIG. 1 is a diagram for explaining an example of a Bayesian network composed of four nodes, and FIG. 2 is a diagram for explaining an example of a conditional probability table at these nodes. A simple Bayesian network composed of nodes S, R, W, and C representing four random variables will be described with reference to FIGS. The random variable S of the node S is “whether the sprinkler has moved”, the random variable R of the node R is “whether it has rained”, the random variable W of the node W is “whether the lawn is wet”, the probability of the node C The variable C represents “whether or not a cloud is present”.

  As shown in FIG. 2, the causal relationship between the four random variables is given as a conditional probability table. FIG. 2 shows an example of a conditional probability table attached to each node of the Bayesian network of FIG. Here, 21 is a conditional probability table associated with the node S, 22 is a conditional probability table associated with the node R, 23 is a conditional probability table associated with the node W, and 24 is a conditional probability table associated with the node C. It is.

  A conditional probability table is data that stores knowledge of the strength of causal relationships between random variables. For example, in the conditional probability table 23 associated with the node W, the conditional probability P (W = no | S = no, R = no) = 0.88 indicates that the lawn does not move when the sprinkler does not move and it does not rain. The probability of not being wet represents the knowledge that it is 0.88. Further, in the conditional probability table 22 associated with the node R, the conditional probability P (R = yes) = 0.02 represents knowledge that the probability of raining (prior probability) is simply 0.02. .

  Next, a concept called MPE (Most Probable Explanation) necessary for explaining the algorithm of the present invention will be briefly described.

ただし、Ｐ（ｈ，ｉ）は集合ｈと集合ｉという値の組み合わせが起きる同時確率で、以下の式で表せる。

ここで、 ｐａｒｅｎｔｓ（ｘ）はノードＸの親ノードの値の組である。 MPE is a set of variable values that best describes given observation data in a Bayesian network. A set of random variables representing given observation data and their values is a set i, and a set of hidden variables (random variables other than observation data) and their values is a set h. Is given by:

However, P (h, i) is a simultaneous probability that a combination of values of the set h and the set i occurs, and can be expressed by the following expression.

Here, parents (x) is a set of values of the parent node of the node X.

For example, assume that the observed value W = yes is given in the Bayesian network of FIG. In this case, the MPE to be obtained is a set {s, r, c} of hidden variables S, R, C having the highest joint probability with the observed value, and is represented by the following expression.

An example of a specific MPE calculation procedure is shown below. First, the simultaneous probability of the set of values “S = no, R = no, C = no” and the observed value W = yes is calculated as follows using the values in the conditional probability table of FIG. The

この中では、「Ｓ＝ｙｅｓ，Ｒ＝ｎｏ，Ｃ＝ｎｏ」がもっとも同時確率の高い値の組み合わせになるので、これがＭＰＥである。したがって、図１および図２の形式で記憶されている知識に基づいて、もし芝生が濡れているならば、「スプリンクラーは動いたが雨は降らず雲も出ていない」という組み合わせがもっとも可能性が高いと推論されたことになる。 Similarly, the simultaneous probabilities of other combinations of values are calculated, and the simultaneous probabilities of all combinations of 2 to the 3rd power are summarized as follows.

Among them, “S = yes, R = no, C = no” is a combination of values having the highest simultaneous probability, and this is MPE. Therefore, based on the knowledge stored in the format of FIG. 1 and FIG. 2, if the lawn is wet, the combination of “the sprinkler moved but it did not rain and no clouds” was most likely Is inferred to be high.

  Next, the learning process of the Bayesian network conditional probability table will be described. If a Bayesian network structure is given and there is a large amount of observation data for each set of random variable values, the values of the elements in the conditional probability table can be determined based on that data. This is called conditional probability table learning.

  For example, out of 1000 observation data, if there are 980 data with R = no, P (R = no) is 980/1000. If there are 686 that have C = no among them, P (C = no | R = no) is 686/980.

  If there is a hidden variable (a variable for which observation data is not given), the value of the conditional probability is determined based on the estimated value of the hidden variable using an EM algorithm or the like.

  As a prior art, an algorithm for learning a mixed model of different Bayesian networks as in Non-Patent Document 4 has been proposed.

  Learning of the conditional probability table is usually performed by processing a large amount of data at a time. However, there is a learning algorithm that sequentially updates the conditional probability table every time new observation data is given. Such an algorithm is called an online learning algorithm.

Next, an online learning algorithm will be described. FIG. 3 is a diagram showing a flowchart of the online learning algorithm. As shown in this flowchart, in the online learning algorithm of the conditional probability table when a hidden variable is included, the learning process is performed by the following processing steps (refer to Non-Patent Document 3 for details). .
Step 1: Set the observed value at the input node.
Step 2: Estimate the value of the hidden variable by calculating the MPE based on the observed value and the current conditional probability table value.
Step 3: Update the conditional probability table based on the MPE value.
Step 4: Output MPE (if necessary).
Step 5: Return to Step 1.

Next, each step of the online learning algorithm flowchart will be described in detail.
In step 1 (31 in FIG. 3), the newly obtained observation data value is set to the value of the input node. Observation data refers to, for example, image information obtained from a camera or the like in the case of an image recognition device, voice information obtained from a microphone or the like in the case of a speech recognition device, or from a text input device or the like in the case of a natural language processing device. In the case of a robot's motion control device, it is information about the external environment and the state of the robot obtained from a sensor or the like.
In step 2 (32 in FIG. 3), using the value of the input data and the value of the conditional probability table at that time, the value of the random variable of a node other than the input node (that is, the hidden node) is calculated by MPE calculation. presume.
In step 3 (33 in FIG. 3), the value of the conditional probability table is recalculated by adding the value of each random variable calculated in step 2 to the statistics of the data obtained in the past. For example, the value of the conditional probability P (Y = yes | X = yes) obtained in the past is 3/10, and the values of the probability variables X and Y obtained this time are X = yes and Y = yes, respectively. If there is, the conditional probability value is updated to P (Y = yes | X = yes) = (3 + 1) / (10 + 1) = 4/11.
In step 4 (34 in FIG. 3), the value of the estimated random variable is output as necessary. For example, the recognition result is output in the case of an image recognition device or a speech recognition device, the information indicating the meaning of a sentence is output in the case of a natural language processing device, and the information necessary for controlling the actuator is output in the case of a motion control device of a robot.

  Various means can be used as means for updating the conditional probability table in step 3. For example, as described in Non-Patent Document 3, using a self-organizing map is one method. In this case, the random variable corresponds to the competitive layer of the self-organizing map, and the value that the random variable can take corresponds to the competitive layer unit of the self-organizing map. The conditional probability corresponds to the value of the element of the reference vector of the unit. By doing so, there is an advantage that the generalization ability is improved by the effect of neighborhood learning which is a feature of the self-organizing map.

  FIG. 4 is a diagram illustrating the module configuration of the probabilistic reasoning / conditional probability learning device. The inference learning apparatus that performs probabilistic inference and conditional probability learning using the online learning algorithm of FIG. 3 can have a module configuration as shown in FIG. In FIG. 4, 41 is an input unit for receiving input data from the outside, and 42 is a knowledge database using a Bayesian network. The probabilistic reasoning unit 43 receives values from the input unit 41 and the knowledge database 42 and performs MPE calculation. The conditional probability table learning unit 44 receives the MPE value from the probabilistic reasoning unit 43 and updates the value of the knowledge database 42 based on the MPE value. The output unit 45 outputs the MPE value received from the probabilistic reasoning unit 43.

  It is also possible to adopt a configuration in which an inference device is obtained by removing the conditional probability table learning unit 44 from the probabilistic inference / conditional probability learning device having the module configuration shown in FIG. A device having such a module configuration is a stochastic reasoning device having no learning function.

  FIG. 5 is a diagram for explaining a module configuration when the online learning algorithm is applied to a robot having learning ability. The online learning algorithm described in FIG. 3 can be applied to a robot having learning ability, for example.

  In this case, when the online learning algorithm in FIG. 3 is applied to a robot having learning ability, an inference learning device having a module configuration as shown in FIG. 5 is obtained. In the apparatus configuration shown in FIG. 5, the probabilistic reasoning unit 53 recognizes the external environment of the robot based on the information from the sensor 51 and the knowledge database 52. The conditional probability table learning unit 54 receives the recognition result from the probabilistic reasoning unit 53 and updates the knowledge database 52 based on the recognition result. Further, the decision making unit 55 makes a decision on exercise based on the recognition result, and drives the actuator 56. At the same time, the decision making unit 55 changes the action rule using a reinforcement learning algorithm or the like.

J. Pearl, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, Morgan Kaufmann, 1988. Ishisugi Hiroshi, “The Elucidation of Information Processing Principles in the Brain”, National Institute of Advanced Industrial Science and Technology Technical Report AIST07-J00012, Mar 2008. Hiroshi Issugi, “Study on Bayesian network structure learning performed by cerebral cortical neural circuit”, Artificial Intelligence Society 72th Artificial Intelligence Basic Problem Study Group (SIG-FPAI) document, Nov 2008. Thiesson B, Meek C, Chickering D, Heckerman D. Learning mixture of DAG models. Technical Report, MSR-TR-97-30, Redmond: Microsoft Research, 1997.

  By the way, when trying to increase the size of the Bayesian network, the number of combinations of node values increases exponentially as the number of nodes increases, so probabilistic reasoning (for example, calculation of posterior probabilities for each random variable and MPE calculation). ) Causes problems such as an increase in the number of meaningless local solutions and an increase in search space. Similarly, when learning the conditional probability table, problems such as overfitting, an increase in the number of meaningless local solutions, and an increase in search space occur. Therefore, the Bayesian network has a problem that it is difficult to increase the scale to a certain extent.

  In addition, a normal Bayesian network has a problem that the mixture distribution cannot be expressed efficiently. The mixed distribution is a probability distribution obtained by mixing a plurality of probability distributions having different shapes. As a specific example, the visual information that enters the retina of a living organism is an example of a signal that follows a mixed distribution. For example, the human face, the shape of a nut, the shape of a predator, etc. generate visual information according to different probability distributions. The visual information presented in front of the eyes of an actual living thing should have generated any one object in front of the eyes. Since the inside of each probability distribution is continuous, learning with a self-organizing map complements and increases generalization ability, but the distribution of distant distributions like the shape of a nut and the shape of a predator increases. Complementing the space is expected to reduce generalization ability.

  Next, an experimental example will be described which shows that the prior art cannot successfully learn the conditional probability table expressing the mixture distribution. FIG. 6 is a diagram for explaining a Bayesian network composed of two hidden nodes and 49 input nodes. FIG. 7 is a diagram for explaining an example in which a mixture distribution is learned using two self-organizing maps using the conventional technique. Please refer to FIG. 6 and FIG.

The Bayesian network described here is a Bayesian network composed of two hidden nodes (H ₁ , H ₂ ) and 49 input nodes (I ₁ ,..., I ₄₉ ) as shown in FIG. Nodes H ₁ and H ₂ are hidden nodes representing hidden variables. Nodes I ₁ ,..., And node I ₄₉ are input nodes for inputting observation data.

  The conditional probability table of the Bayesian network in FIG. 6 is learned by using a conventional technique using a self-organizing map described in Non-Patent Document 3, for example. In this learning device, two-dimensional data generated from a mixed distribution obtained by mixing two probability distributions is converted into 49-dimensional redundant data and given as an observation value of an input node. All random variables have 10 possible values.

Conversion from two-dimensional data to 49-dimensional data is performed as follows. The two-dimensional space is divided by a 7 × 7 grid, and the Euclidean distance between the coordinates of the 49 grid points and the coordinates of the input two-dimensional data is d _i (i = 1,..., 49), and a _i = A value obtained by quantizing max (0.8-3d _i , 0) into 10 levels is set as a value of each input node. However, max (x, y) is a function that returns the maximum value of x and y.

  In an example in which a mixture distribution is learned using two self-organizing maps according to the prior art, as shown in FIG. 7, the result of the experiment is a probability distribution in which two nodes (self-organizing maps) are separated by two. I will forcibly learn at the same time. For this reason, there is a problem that a meaningless learning result is obtained as a result.

  In FIG. 7, an L-shaped portion (region) surrounded by a frame indicates a probability distribution for generating input data on a two-dimensional space. The point on the broken line and the point on the solid line indicate the centroid of the receptive field of each unit of the self-organizing map of the two nodes.

  There are conventional techniques that can handle mixed distributions. For example, Non-Patent Document 4 is a conventional technique for expressing a mixture distribution with a Bayesian network. However, the Bayesian network problem, which is difficult to scale up, remains unsolved.

  The present invention has been made to solve the above-described problems, and an object of the present invention is to perform inference processing using a Bayesian network having a mechanism for limiting combinations of possible values of nodes representing random variables. It is an object of the present invention to provide a stochastic reasoning apparatus that efficiently performs the above.

  In order to achieve the above object, a stochastic reasoning apparatus according to the present invention basically has a network configuration with a plurality of nodes representing random variables and edges representing causal relationships between the random variables between the nodes. In a probabilistic inference device equipped with an inference mechanism that performs inference processing using the Bayesian network, adding constraints to the combination of values in this Bayesian network reduces the degree of freedom of the combination of values, Resolve. The technical means for constraining the value is to add a constraint node to the Bayesian network, or equivalently, but how much the constraint is satisfied when calculating the joint probability. The method of reflecting on the size is used.

  Specifically, as a first feature, the stochastic inference apparatus of the present invention has an inference mechanism that performs an inference process using a Bayesian network having a mechanism for limiting combinations of values that can be taken by nodes representing random variables. The Bayesian network is a probabilistic inference device, wherein a possible value of a node representing a random variable is selected from among three or more values including a value called two or more normal values and one or more φ values. There are two or more nodes that take any one of the nodes constituting the network, and there are one or more nodes called constraint nodes as child nodes of the node that can take a φ value. The value of the conditional probability table of the condition node is a Bayesian network that restricts the value of the node that can take the φ value to be high in frequency of taking the φ value, and the inference mechanism is a part of the Bayesian network. When a node is given as input the value of the random variable represented by the node or the probability distribution of the value, the posterior probabilities of the values or values of other random variables are inferred using the network of nodes constituting the Bayesian network. It is characterized by this.

  As a second feature, the stochastic inference apparatus according to the present invention is such that the Bayesian network is a node that can further take a φ value, and the number of values other than the φ value of the node is s. , A Bayesian network having one or more nodes with substantially equal prior probabilities taking each of the s values, and the inference mechanism includes the random variables represented by the nodes at some nodes of the Bayesian network. When a value or a probability distribution of values is given as an input, a value of another random variable or a posteriori probability of the value is inferred using a network of nodes constituting a Bayesian network.

  As a third feature, in the probabilistic inference apparatus according to the present invention, the conditional probability table of each node is obtained when the conditional probability table is learned using the inference result obtained by performing the inference processing. A conditional probability table of one or more nodes that can take a value is learned using a self-organizing map, and values other than two or more φ values that can be taken by the node at that time are subject to neighborhood learning It is characterized by that.

  According to the probabilistic inference apparatus of the present invention having the above-described features, by adding a constraint condition to the combination of values of the Bayesian network, the degree of freedom of the combination of values is reduced, and the inference processing is efficiently performed. Can be done well. By adding constraints, the expressive power of a Bayesian network is reduced, but image information and audio information in the natural world satisfy the property that the signal source is sparse, that is, rarely activated. Therefore, there is no problem in practicality. The Bayesian network in the stochastic reasoning apparatus according to the present invention uses a Bayesian network specialized to handle such information in the natural world more efficiently. This also solves the problem of mixture distribution.

  In this way, the number of combinations of node values is drastically reduced due to the constraints, which dramatically reduces the amount of computation when inferring the value of a random variable. As shown in FIG. 12), the mixture distribution can be expressed well.

It is a figure explaining an example of the Bayesian network which consists of four nodes. It is a figure explaining an example of the conditional probability table in a node. It is a figure which shows the flowchart of an online learning algorithm. It is a figure explaining the module structure of a stochastic reasoning and conditional probability learning apparatus. It is a figure explaining the module structure at the time of applying an online learning algorithm to the robot with learning ability. It is a figure explaining the Bayesian network which consists of two hidden nodes and 49 input nodes. It is a figure explaining an example which learned mixture distribution using two self-organizing maps using conventional technology. It is a figure explaining the Bayesian network with the node S which restrict | limits the combination of the value of a hidden variable. It is a figure explaining an example of the storage format of the conditional probability table | surface of a Bayesian network used in the stochastic reasoning apparatus of this invention. It is a figure explaining the example of the Bayesian network in which some hidden variables are not restricted by the φ value. It is a figure explaining the example of the Bayesian network which has two constraint condition nodes. It is a figure explaining an example which learned mixture distribution using two self-organization maps using the present invention.

  Hereinafter, modes for carrying out the present invention will be described. First, a Bayesian network having nodes S that limit combinations of variable values will be described. FIG. 8 is a diagram for explaining a Bayesian network having nodes S that limit combinations of variable values.

Nodes H _i (i = 1,..., n) representing n hidden variables have (s + 1) values {x _φ , x ₁ , x ₂ ,..., x _s−1 , x _s }, respectively. It can be taken. Hereinafter, _xφ is called a φ value, and values other than the φ value are called non-φ values.

  Further, as in the Bayesian network shown in FIG. 8, one node S expressing a constraint condition that increases the probability that the value of each hidden variable becomes a φ value is added as a child node of all hidden variables. This node S is called a constraint node.

The conditional probability table associated with the node S of the constraint condition node indicates that the conditional probability P (S = yes | H ₁ ,..., H _n ) when many of the parent nodes H _i of the node S take φ values. Assume that the value is large. The value of the conditional probability represents the extent to which the set of hidden variable values satisfies the constraint condition. With such a feature, when the value of the input node I _j (j = 1,..., M) is given, the value of S = yes is given at the same time, and the value of the hidden variable H _i is calculated by MPE. As a result, the value of the hidden variable takes a φ value with high frequency.

これを例えば、以下の式に修正する。

このように修正した場合、明示的に下記の条件付確率表Ｐ（Ｓ＝ｙｅｓ｜Ｈ_１，…，Ｈ_ｎ）を持つ制約条件ノードを追加した場合と、実質的に等価である。

ただし、αは正規化定数、βはスパース性を制御するパラメタである。Ａ（ｈ）はｈの活性度を表す値である。以下に定義されるＡ（ｈ）は「非φ値を取る要素の数」がｍ個であれば１、ｍ個でなければ無限大を示す値（所定値）を返す。

The node S and its conditional probability table P (S | H ₁ ,..., H _n ) do not have to be explicitly stored in the memory, and substantially the same effect can be obtained only by correcting the joint probability calculation formula. can get. The equation for calculating the joint probability in a Bayesian network that does not include the node S of the constraint condition node was as follows.

For example, this is corrected to the following formula.

Such a modification is substantially equivalent to the case where a constraint node having the following conditional probability table P (S = yes | H ₁ ,..., H _n ) is explicitly added.

Where α is a normalization constant and β is a parameter for controlling sparsity. A (h) is a value representing the activity of h. A (h) defined below returns 1 if the “number of elements having non-φ values” is m, and returns a value (predetermined value) indicating infinity if the number is not m.

  When the node S of the constraint condition node defined in this way is added to the Bayesian network, many of the values of the hidden variables are constrained to take the φ value during the MPE calculation. Specifically, of the n hidden nodes, the constraint condition is that m takes a non-φ value and (n−m) takes a φ value.

At this time, the number of combinations of values that can be taken by n nodes is _n C _m multiplied by s multiplied by _m (where _n C _m is the number of combinations for selecting m from n). When there is no constraint condition, the number of value combinations is s + 1 to the nth power, and the number of value combinations is dramatically reduced by the constraint condition. This effect becomes more prominent when the number of nodes n is large.

  This effect solves the problem that it is difficult to increase the scale of the Bayesian network. FIG. 9 is a diagram for explaining an example of the storage format of the Bayesian network conditional probability table used in the stochastic inference apparatus of the present invention.

  The Bayesian network in the probabilistic reasoning apparatus of the present invention can hold the conditional probability table of nodes other than the node S of the constraint condition node in the same format as in the prior art. For example, when X and Y are random variables, the conditional probability P (Y | X) is specifically expressed as (s + 1) × (s + 1) conditions as shown in the conditional probability table 91 shown in FIG. A table of attached probability values may be recorded on the memory.

  Note that the fact that most nodes take a φ value is an essential requirement to suppress the explosion of value combinations, so even a Bayesian network where a small number of nodes are not constrained naturally. Included in the invention.

FIG. 10 is a diagram illustrating an example of a Bayesian network in which some hidden variables are not restricted by the φ value. For example, FIG. 10 shows an example of a Bayesian network in which some nodes are not restricted by the φ value. In this Bayesian network, the random variable H ₁ and the random variable H ₃ are constrained by the node S to take the φ value with high frequency, but the random variable H ₂ is not subject to such a constraint. Even in such a case, the combination of values that the random variable can take is still drastically reduced, and the effect of the invention is not lost.

Also, there is no need for one constraint node. FIG. 11 is a diagram illustrating an example of a Bayesian network having two constraint condition nodes. In the example shown in FIG. 11, the node S ₁ and node S ₂ are both constraint nodes. The node S ₁ has a role of restricting the values of the random variable H ₁ and the random variable H ₂ and the node S ₂ to restrict the values of the random variable H ₃ and the random variable H ₄ to φ values with high frequency.

In addition, in the function A (h) defined above, the constraint condition that the number of nodes taking the φ value is a fixed value of (n−m) is considered, but the node that takes the φ value for each given observation data Even a Bayesian network whose number fluctuates is included in the present invention. For example, this is the case when probabilistic inference is executed in the form of an optimization problem having the number of nodes having a value other than φ as a fine term. Specifically, for example, the case where the function A (h) is defined as follows is included.

  In the example of MPE calculation described so far, one definite value is input to one input node. However, in general, in a Bayesian network, observation data given to a node does not need to be a definite value, and even when a probability distribution of values is given, probabilistic inference regarding the values of other random variables can be performed.

  The probabilistic reasoning apparatus of the present invention is effective not only in the probability calculation by MPE calculation but also in performing various probabilistic inferences such as calculation of posterior probabilities of random variables.

  There are various methods for calculating the MPE. Regardless of the algorithm used there, the effect is exhibited by using the Bayesian network by the stochastic reasoning apparatus of the present invention. The algorithms used include not only the simple method of calculating all combinations of values described above, but also search methods using heuristics such as best-first search, methods using dynamic programming such as the Viterbi algorithm, and greedy It also includes methods using local search methods such as the method, steepest descent method, simulated annealing method, and Monte Carlo methods such as Markov chain Monte Carlo.

  Similarly, when a posterior probability calculation of a random variable is used using a Bayesian network, there is an effect regardless of the algorithm used. The algorithm used is a simple method that uses the joint probability of all combinations of values, a method that uses heuristics, a method that uses dynamic programming such as a probability propagation algorithm, and the loopy probability propagation algorithm that is an approximate solution that applies it. And a method using a Monte Carlo method such as Markov chain Monte Carlo.

  A conditional probability table learning device that learns a conditional probability table using the inference result of the probabilistic inference device described above can be constructed. Specifically, one method is to use the online learning algorithm described in FIG. 3, but an EM algorithm or the like can be used in addition to the algorithm in FIG.

  Furthermore, a self-organizing map obtained by the method described in Non-Patent Document 3 can be used when learning conditional probabilities. However, the φ value is not subject to neighborhood learning. That is, it is assumed that the unit representing the φ value is not in the vicinity of other units representing values other than the φ value, and is configured to perform neighborhood learning.

  That is, when learning a conditional probability table using an inference result of a probabilistic inference device, the conditional probability table of one or more nodes that can take a φ value is learned using a self-organizing map. In this case, a conditional probability table learning device is provided that uses values other than two or more φ values among the values that can be taken by the node at that time as targets of neighborhood learning.

  A Bayesian network obtained as a learning result using such a learning algorithm is the node that can take a φ value, and when the number of values other than the φ value of the node is s, A Bayesian network having one or more nodes with substantially equal prior probabilities for each value is obtained.

Specifically, in the self-organizing map, the probability of each unit in the competitive layer becoming a winner is almost equal due to the effects of neighborhood learning and competitive learning. For example, the value that the random variable X can take is
{X _φ , x ₁ , x ₂ ,..., X _s }
, The prior probabilities P (X = x _i ) (i = 1,..., S) taking each value other than the φ value by making other than the φ value x _φ an object of neighborhood learning,
P (X = x ₁ ) = P (X = x ₂ ) =... = P (X = x _s ) = δ _X
The following equation holds approximately. However, the [delta] _X is a value determined for each node.

If this equation holds, for two random variables X and Y,
P (X | Y) = P (X)
There is an advantage that it is easy to determine whether or not the relationship is established. Conditional probability P | value of (X Y) is because it is only necessary to determine whether substantially equal to [delta] _X. This property is useful for simplifying Bayesian networks and increasing computational efficiency. Also, if the node X does not have a parent node, the value of the prior probability P (X) is [delta] _X with respect to non-φ value, the prior probability of the individual values _{P (X = x 1),} P (X = X ₂ ),..., P (X = x _s ) has the advantage of not having to be explicitly stored in the memory.

  In general, in machine learning algorithms, when the degree of freedom of parameters is high, there is a problem that generalization ability tends to be reduced due to overfitting and local solutions, but in the Bayesian network of the stochastic reasoning apparatus of the present invention, random variables By limiting the combinations of values, the values that can be taken by the elements of the conditional probability table are also constrained, so it can be expected that generalization ability will be improved by bypassing overfitting and local solutions.

  Limiting the value of the random variable may lead to a reduction in the amount of memory when storing the table. If the value of many elements of the conditional probability table becomes 0 by limiting the value, it is necessary to store the conditional probability table by using a data structure that assumes such a sparse table. The amount of memory can be reduced.

  In some cases, limiting the value of a random variable may solve the problem of floating point overflow / underflow in posterior probability calculations and the problem of calculation accuracy. In order to perform probabilistic reasoning on a large-scale Bayesian network, it is necessary to perform a very large number of multiplications, which causes problems such as overflow / underflow and poor calculation accuracy. If the probabilistic reasoning algorithm used has the property that “φ value nodes can be ignored”, probabilistic reasoning can be performed using only a small number of non-φ value nodes, thus avoiding these problems. Can do.

As in the previous experiment, the conditional probability table for the same input data as in the previous experiment was learned in a Bayesian network composed of two hidden nodes and 49 input nodes as described with reference to FIG. However, m = 1, that is, in MPE, a constraint was imposed so that one of the two was always a φ value and one was a non-φ value. That is, the experiment was performed under conditions equivalent to the case where the constraint node S was added as a common child node of the _two hidden nodes H ₁ and H ₂ in FIG.

  The point that the two hidden nodes each operate as a competitive layer of the self-organizing map at the time of learning is the same as the above-described experiment. However, the φ value is not subject to neighborhood learning. That is, the neighborhood learning is performed on the assumption that the unit representing the φ value is not in the vicinity of all values representing values other than the other φ values.

  The result of the experiment is shown in FIG. FIG. 12 is a diagram for explaining an example in which a mixture distribution is learned using two self-organizing maps using the probabilistic reasoning apparatus of the present invention. In the experimental result shown in FIG. 12, when one point in the left L-shaped probability distribution is input, one of the two nodes becomes a non-φ value, and the other node has the right L-shaped. A conditional probability table that has non-φ values is learned. As a result, the two one-dimensional self-organizing maps clearly learn the two probability distributions.

In this experiment, the number of values that each node can take is s + 1 = 10. Without constraints, the number of value combinations is (s + 1) squared, ie, 100, but thanks to the constraints, s is multiplied by ₂ C ₁ , ie, 18 The calculation speed of MPE has been greatly improved. If the Bayesian network becomes larger, the effect of improving the calculation speed becomes more prominent.

  As described in Non-Patent Document 2, probabilistic inference devices using Bayesian networks include pattern recognition (image recognition, speech recognition, etc.), robot motion control and action planning, fuzzy information processing, natural language processing, etc. Can be used for various purposes.

  The probabilistic reasoning apparatus of the present invention is effective for many Bayesian network applications including them. In particular, for example, it is highly effective in processing such as pattern recognition of information in the natural world that is good at handling the human brain, specifically, information such as natural images, audio information, and natural language.

21-24 Conditional probability table 41 Input unit 42 Knowledge database 43 Probabilistic reasoning unit 44 Conditional probability table learning unit 45 Output unit 51 Sensor 52 Knowledge database 53 Probabilistic reasoning unit 54 Conditional probability table learning unit 55 Decision making unit 56 Actuator 91 Conditional probability table

Claims (3)

A stochastic inference apparatus having an inference mechanism that performs an inference process using a Bayesian network having a mechanism that limits combinations of possible values of nodes representing random variables,
In the Bayesian network, a node representing a random variable has a node that takes one of three or more values including two or more normal values and one or more values called φ values. There are one or more nodes called constraint nodes as child nodes of the node that exist in two or more nodes constituting the network and can take a φ value, and the conditional probability table of the constraint node The value is a Bayesian network that constrains the value of the node that can take a φ value so that the frequency of taking the φ value is high,
When the inference mechanism receives a value of a random variable represented by the node or a probability distribution of the value as an input to a part of the nodes of the Bayesian network, the inference mechanism uses another network of nodes constituting the Bayesian network to A stochastic reasoning device for inferring a value of a random variable or a posteriori probability of a value. The stochastic inference device according to claim 1,
The Bayesian network further includes:
the node that can take a φ value,
When the number of values other than the φ value of the node is s,
A Bayesian network having one or more nodes with substantially equal prior probabilities for each of the s values,
When the inference mechanism receives a value of a random variable represented by the node or a probability distribution of the value as an input to a part of the nodes of the Bayesian network, the inference mechanism uses another network of nodes constituting the Bayesian network to A stochastic reasoning device for inferring a value of a random variable or a posteriori probability of a value. In the probabilistic inference device according to claim 1 or 2,
The conditional probability table for each node is self-organizing the conditional probability table for one or more nodes that can take a φ value when learning the conditional probability table using the inference result obtained by the inference process. A probabilistic inference device characterized by learning using a map, and using values other than two or more φ values among values that can be taken by the node at that time as targets for neighborhood learning.

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