Patent Document ID: 9489632
Application ID: 14066265
Patent Status: 1

Claim One:
1. A model estimation device including a central processing unit, comprising: a data input unit which acquires observed value data subjected to estimation of a latent variable model, a type of each component constituting the latent variable model, and a state number candidate set of the latent variable model; a state number setting unit which sets an element for which computation has not been completed yet in the state number candidate set, as the number of states; an initialization unit which sets initial values of a variational probability of a latent variable, a parameter, and the type of each component; a latent variable variational probability computation unit which acquires the observed value data and the variational probability of the latent variable, the type of each component, and the parameter set by the initialization unit, and computes the variational probability of the latent variable so as to maximize a lower bound of a marginal model posterior probability; a component optimization unit which acquires the observed value data and the variational probability of the latent variable, the type of each component, and the parameter set by the initialization unit, and estimates an optimal type of each component and a parameter thereof by optimizing the type of each component and the parameter so as to maximize the lower bound of the marginal model posterior probability separated for each component of the latent variable model; an optimality determination unit which acquires the observed value data, the type of each component and the parameter thereof estimated by the component optimization unit, and the variational probability of the latent variable computed by the latent variable variational probability computation unit, and determining whether or not to continue the maximization of the lower bound of the marginal model posterior probability; and a result output unit which outputs the variational probability of the latent variable computed by the latent variable variational probability computation unit and the type of each component and the parameter thereof estimated by the component optimization unit, wherein: the marginal model posterior probability is calculated about a probability distribution so that a parameter θ i increases when a sample is removed by integral calculus in a prior distribution, where the observed value is denoted by x ij represented as in the following Expression (1), 
 x ij iε{1,. .. , N}, jε{1,. .. , N i }  (1) the latent variable is denoted by z ij , corresponding to the observed value, represented as in the following Expression (2), where K is the number of types of latent states and k is the component, z ij ∈ { 0 , 1 } K , ∑ k ⁢ z ij , k = 1 ( 2 ) suppose the observed variable x ij is created from a regular model that differs according to the value of the latent variable z ij , in this case, the observed variable x ij is represented as in the following Expression (3), wherein φ means a parameter of a probability model, 
 x ij ˜P k ( x ij |φ (k) ) if z ij,k =1  (3) several types of models are assumed for P k shown in Expression (3), wherein P k is the conditional probability of x ij given φ (k) , where the types are denoted by H, the models are denoted by M, a parameter for determining the creation of the latent variable z ij is denoted by θ i (where latent variables are created from the same parameter for each i), it is assumed that z ij is created from a given regular model, in this case, z ij is represented as in the following Expression (4), 
 z ij ˜P ( z ij |θ i )  (4) where P is the conditional probability of z ij given θ i and it is assumed that p(z ij |α) which is a prior distribution having a parameter α and corresponds to z ij marginalizing θ i is analytically computed as shown in the following Expression (5) and is a regular model, p ⁡ ( z ij | α ) = ∫ ∏ f ⁢ ⁢ p ⁡ ( z ij | θ i ) ⁢ p ⁡ ( θ i | α ) ⁢ ⅆ α ( 5 ) the marginal model posterior probability is represented as in the following Expression (7-3), derived by substituting the Expression (7-1) into the Expression (7-2), p ⁡ ( z t · | α ) = ∫ ∏ i ⁢ ⁢ p ⁡ ( z ij | θ t ) ⁢ p ⁡ ( θ t | α ) ⁢ ⁢ ⅆ α ( 7 - 1 ) log ⁢ ⁢ p ⁡ ( x | M ) = log ⁢ ⁢ ∑ z ⁢ ∫ p ⁡ ( x , z , θ , ϕ , α ) ⁢ ⅆ θ ⁢ ⅆ φ ⁢ ⅆ α = log ⁢ ⁢ ∑ z ⁢ ∫ p ⁡ ( x | z , ϕ ) ⁢ p ⁡ ( z | θ , α ) ⁢ p ⁡ ( θ ) ⁢ p ⁡ ( ϕ , α ) ⁢ ⅆ θ ⁢ ⅆ φ ⁢ ⅆ α ( 7 - 2 ) log ⁢ ⁢ p ⁡ ( x N | M ) = log ⁢ ⁢ ∑ z ⁢ ∫ p ⁡ ( ϕ , α ) ⁢ ∏ i ⁢ ⁢ p ⁡ ( z i · | α ) ⁢ ∏ j ⁢ ⁢ p ⁡ ( x ij | z ij , ϕ ) ⁢ ⅆ ϕ ⁢ ⅆ α. ( 7 - 3 )