KR102403797B1 - Method and apparatus for adversarial likelihood-free inference on black-box generator - Google Patents

Abstract

) 및 확률적 인코더 네트워크(probabilistic encoder network:

)에 대해서, 메트로폴리스-해스팅 알고리즘을 m번 반복하는 단계 - 여기서 m은 매트로폴리스-해스팅 알고리즘의 고정(stationary) 분포에 대한 수렴 속도를 제어하는 탐사-발산 하이퍼 파라미터(exploration-expoitation hyperparameter)임 -; 블랙박스 생성 모델에 입력변수를 대입한 출력값을 산출하는 단계; 제1 경사 하강(gradient) 기법에 기초하여 상기 판별자 네트워크를 l 번 업데이트 하는 단계; 및 제2 경사 하강(gradient) 기법에 기초하여 상기 확률적 인코더 네트워크를 l 번 업데이트 하는 단계를 포함할 수 있다. According to an aspect of the present disclosure, there is provided a method for inferring adversarial non-likelihood for a black box generator, performed on a computer system. The method described above is a discriminator network (discriminator network:

) and a probabilistic encoder network:

), repeat the metropolis-Hasting algorithm m times, where m is the exploration-expoitation hyperparameter that controls the convergence rate for the stationary distribution of the metropolis-Hasting algorithm. -; calculating an output value obtained by substituting input variables into the black box generation model; updating the discriminator network l times based on a first gradient descent technique; and updating the probabilistic encoder network l times based on a second gradient descent technique.

Description

Adversarial non-likelihood inference method and apparatus for black box generator

The present disclosure relates to an adversarial non-likelihood inference method for a black box generator.

Recently, generative adversarial networks (GANs) have been recently emphasized in terms of their success in estimating data distribution implicitly. In GAN, the generator is trained jointly with the discriminator, so the generator can be a learnable and fine-tuneable model according to the adversarial learning mechanism. In contrast to these generators integrated into adversarial frameworks, efforts have been made to incorporate the implicit data estimation function of GANs as generators that cannot be integrated with the adversarial frameworks of GANs. For example, a simulation model can be considered a generator that is not integrated into the GAN learning structure, and researchers have been interested in estimating the actual parameters of the simulation model through non-reproducible mechanistic data (Meeds & Welling, 2015; Gutmann & Corander, 2016; Louppe et al., 2019).

Before proceeding, we can define a black box generation model to clearly indicate the types of generators we are interested in. The black box generative model represents a generative model with three characteristics. First, the internal process of the black box model is determined before the inference step, and is designed by domain experts or other statistical models. Second, the coefficients of the internal process are not changed in the reasoning stage because the coefficients are obtained through domain-specific knowledge or a separate learning process. Third, internal variables following an unknown distribution exist inside the generative model, resulting in variability in model results. For example, continuous, discontinuous and agent-based simulation models can be black box generators that generate stochastic trajectories of modeled states. As another example, a pre-trained and fixed de-convolutional neural network may be another practical example of a black box generator.

를 유추하여 생성화될 수 있다. 여기서

는 모델 입력 매개 변수이고

는 재구성할 관찰된 데이터이다. 그러나,이 베이지안 추론 문제는 다루기 힘든 우도

에 의해 어려움을 겪는데, 여기서 어려움은 잡음 변수(nuisance variable)

가 추론 과정에서 접근하기 어렵다는 블랙 박스 특성으로 인해 발생할 수 있다. 여기서 잡음 변수

는 같은 입력 변수를 입력한다 해도 생성기의 출력에 랜덤성을 부여하는, 생성기에 내재하는 관측 불가능한 제어 변수이다. The study of black box generators emphasizes the re-generation of observations, which are posterior distributions.

can be generated by analogy with here

is the model input parameter and

is the observed data to be reconstructed. However, this Bayesian inference problem has an intractable likelihood

difficulty is caused by the noise variable

It may be caused by the black box characteristic that is difficult to access in the inference process. where the noise variable

is an unobservable control variable inherent in the generator that gives randomness to the output of the generator even when the same input variable is input.

의 도함수를 계산할 수 없기 때문에 최종 신호 피드백을 역 전파 할 수 없게 된다. 역 전파가 불가능하다는 것은 신경망 모델과 함께 블랙 박스 생성기의 사용을 방지한다. 역 전파 문제를 극복하기 위해 Louppe et al. (2019)는 적대적 설정에서 블랙 박스 모델에 대한 비우도 추론의 최적화 알고리즘인 AVO (Adversarial Variational Optimization)를 제안한다. Louppe et al. (2019)는 역 전파 문제를 해결하기 위해 블랙 박스 모델의 입력 매개 변수 분포로 제안 분포(proposal distribution)

를 제안한다. 그러나 이 솔루션 개념에서 AVO는 사후 분포가 제안된 분포라고 가정하는데, 이는 보장 할 수 없으므로, AVO는 역 전파에서 잠재적으로 부정확한 분포 하에서 매개 변수를 최적화한다.Besides the inference difficulties that arise from not being able to access u, the derivative of the posterior likelihood cannot be computed as Like this, Udo

Since the derivative of cannot be computed, it becomes impossible to backpropagate the final signal feedback. The impossibility of backpropagation prevents the use of black box generators with neural network models. To overcome the backpropagation problem, Louppe et al. (2019) proposes Adversarial Variational Optimization (AVO), an optimization algorithm of non-likelihood inference for black box models in adversarial settings. Louppe et al. (2019) proposed a distribution as an input parameter distribution of a black box model to solve the backpropagation problem.

suggest However, in this solution concept, AVO assumes that the posterior distribution is the proposed distribution, which cannot be guaranteed, so AVO optimizes parameters under potentially imprecise distributions in backpropagation.

를 사용하는 대신 역 전파 문제를 피하기 위해 확률적 엔코더 네트워크라고 하는 보조 구조를 사용한다. 확률적 엔코더 네트워크는 확률적 프로세스에서 샘플링된 결과를 갖는 판별자의 확률 모델을 가정합니다. 블랙 박스 생성 모델의 기본 매개 변수를 추정하기 위해 기본 알고리즘으로 ALFI를 테스트할 수 있다. 결과적으로 제한된 시뮬레이션 예산으로 ALFI가 최상의 추정 정확도를 달성함을 보여준다.The present disclosure starts with the potential problem of AVO given sparse observations, and we propose a new adversarial framework for inference on black box generative models, a new Adversarial Likelihood-Free Inference (ALFI). do. ALFI attempts to extend the boundaries of adversarial frameworks from implicit neural network generation models with large data sets to general black box generation models with sparse observations, which originate from other domains. ALFI is the proposed distribution

Instead of using , we use an auxiliary structure called a probabilistic encoder network to avoid the backpropagation problem. A probabilistic encoder network assumes a probabilistic model of a discriminator with sampled results from a probabilistic process. ALFI can be tested with the basic algorithm to estimate the basic parameters of the black box generation model. As a result, we show that ALFI achieves the best estimation accuracy with a limited simulation budget.

Therefore, there is a need to increase the estimation accuracy with a limited simulation budget.

) 및 확률적 인코더 네트워크(probabilistic encoder network:

)에 대해서, 메트로폴리스-해스팅 알고리즘을 m번 반복하는 단계 - 여기서 m은 매트로폴리스-해스팅 알고리즘의 고정(stationary) 분포에 대한 수렴 속도를 제어하는 탐사-발산 하이퍼 파라미터(exploration-expoitation hyperparameter)임 -; 블랙박스 생성 모델에 입력변수를 대입한 출력값을 산출하는 단계; 제1 경사 하강(gradient) 기법에 기초하여 상기 판별자 네트워크를 l 번 업데이트 하는 단계; 및 제2 경사 하강(gradient) 기법에 기초하여 상기 확률적 인코더 네트워크를 l 번 업데이트 하는 단계를 포함할 수 있다. According to an aspect of the present disclosure, there is provided a method for inferring adversarial non-likelihood for a black box generator, performed on a computer system. The method described above is a discriminator network (discriminator network:

) and a probabilistic encoder network:

), repeat the metropolis-Hasting algorithm m times, where m is the exploration-expoitation hyperparameter that controls the convergence rate for the stationary distribution of the metropolis-Hasting algorithm. -; calculating an output value obtained by substituting input variables into the black box generation model; updating the discriminator network l times based on a first gradient descent technique; and updating the probabilistic encoder network l times based on a second gradient descent technique.

In an embodiment of the present disclosure, repeating the metropolis-hasting algorithm m times may be calculated using input variables of the following black box generation model.

In an embodiment of the present disclosure, the first gradient descent technique may be learned to optimize Equation (3) below.

Formula (3):

In an embodiment of the present disclosure, the second gradient descent technique may be learned to optimize Equation (4) below.

Formula (4):

In an embodiment of the present disclosure, Equation (4) may be learned in a direction to optimize likelihood to infer a random variable generated from a discriminator.

) 및 확률적 인코더 네트워크(probabilistic encoder network:

)에 대해서, 메트로폴리스-해스팅 알고리즘을 m번 반복하도록 구성되고 - 여기서 m은 매트로폴리스-해스팅 알고리즘의 고정(stationary) 분포에 대한 수렴 속도를 제어하는 탐사-발산 하이퍼 파라미터(exploration-expoitation hyperparameter)임 -; 블랙박스 생성 모델에 입력변수를 대입한 출력값을 산출하도록 구성되며; 제1 경사 하강(gradient) 기법에 기초하여 상기 판별자 네트워크를 l 번 업데이트하도록 구성되고 제2 경사 하강(gradient) 기법에 기초하여 상기 확률적 인코더 네트워크를 l 번 업데이트하도록 구성될 수 있다. According to another feature of the present disclosure, an apparatus configured to provide adversarial non-likelihood inference for a black box generator is provided. The device includes a computing module, the computing module comprising a discriminator network (discriminator network:

) and a probabilistic encoder network:

), configured to iterate the metropolis-Hasting algorithm m times - where m is an exploration-expoitation hyperparameter that controls the rate of convergence for a stationary distribution of the metropolis-Hasting algorithm. lim -; configured to calculate an output value by substituting input variables into the black box generation model; update the discriminator network l times based on a first gradient descent technique and update the probabilistic encoder network l times based on a second gradient descent technique.

According to another feature of the present disclosure, there is provided a computer-readable recording medium containing one or more computer-readable instructions executable by a computer, wherein the one or more computer-readable instructions, when executed by the computer, cause the computer to , a computer-readable recording medium for performing the above-described method may be provided.

According to an embodiment of the present disclosure, it is possible to provide the best estimation accuracy with a limited simulation budget.

=0.001인 Rejection ABC 에 의해 얻어지는 멀티 모달 기준 사후 분포를 캡처하지 못하는 반면, ALFI는 멀티 모달 분포를 유추하는데 성공하는 것을 도시하는 도면이다.
도 2(a) 내지 (c)는 본 개시의 일 실시예에 따라 GAN, AVO 및 ALFI에 대한 네트워크 구조 비교하는 도면이다.
도 3은 본 개시의 일 실시예에 따라 GAN, AVO 및 ALFI에 대한 확률적 그래피컬 모델(PGM)을 비교하는 도면이다.
도 4(a) 내지 (c)는 본 개시의 일 실시예에 따라 예시적인 모델을 도시하는 그래프이다.
도 5는 본 개시의 일 실시예에 따라 ALFI 및 5 개의 기준을 성능 비교하는 그래프이다.
도 6은 관측이 도 6(a)와 같을 때의 포아송 시뮬레이션 결과를 도시하는 도면이다.
도 7은 본 개시의 일 실시예에 따라, 실제 샘플과 상기 실제 샘플의 마스크 된 관측 값을 한 쌍으로 도시하는 도면이다. 1 is an AVO in an implicit proposal network according to an embodiment of the present disclosure;

A diagram showing that ALFI succeeds in inferring a multi-modal distribution, while failing to capture the multi-modal reference posterior distribution obtained by Rejection ABC =0.001.
2(a) to (c) are diagrams comparing network structures for GAN, AVO, and ALFI according to an embodiment of the present disclosure.
3 is a diagram comparing probabilistic graphical models (PGMs) for GAN, AVO, and ALFI according to an embodiment of the present disclosure.
4(a) to (c) are graphs illustrating an exemplary model according to an embodiment of the present disclosure.
5 is a graph comparing performance of ALFI and five criteria according to an embodiment of the present disclosure.
FIG. 6 is a diagram showing a Poisson simulation result when the observation is the same as that of FIG. 6(a).
7 is a diagram illustrating a pair of a real sample and a masked observation value of the real sample, according to an embodiment of the present disclosure.

Hereinafter, embodiments of the present disclosure will be described in detail with reference to the accompanying drawings. Hereinafter, when it is determined that there is a risk of unnecessarily obscuring the subject matter of the present disclosure, detailed descriptions of already known functions and configurations will be omitted. In addition, it should be understood that the contents described below are only related to one embodiment of the present disclosure, and the present disclosure is not limited thereto.

The terms used in the present disclosure are only used to describe specific embodiments and are not intended to limit the present disclosure. For example, an element expressed in a singular should be understood as a concept including a plurality of elements unless the context clearly means only the singular. It should be understood that the term "and/or" as used in this disclosure is intended to encompass any and all possible combinations by one or more of the listed items. Terms such as 'comprise' or 'have' used in the present disclosure are only intended to designate that the features, numbers, steps, operations, components, parts, or combinations thereof described in the present disclosure exist, and the terms It is not intended to exclude the possibility of addition or existence of one or more other features or numbers, steps, operations, components, parts, or combinations thereof.

In an embodiment of the present disclosure, a 'module' or 'unit' means a functional part that performs at least one function or operation, and may be implemented as hardware or software, or a combination of hardware and software. In addition, the plurality of 'modules' or 'units' may be integrated into at least one software module and implemented by at least one processor, except for 'modules' or 'units' that need to be implemented with specific hardware. have.

Hereinafter, with reference to the accompanying drawings, an embodiment of the present disclosure will be described in detail.

Generative adversarial networks (GANs) are considered as implicit estimators of data distribution, and this perspective is the motivation for using GANs in real parameter estimation under complex black box generative models. to give Previous studies have investigated a method to back propagate gradients through a black box model, but this disclosure proposes an augmented neural structure to perform non-likelihood inference on a black box model. . In more detail, we propose Adversarial Likelihood-Free Inference (ALFI), a new adversarial framework using beta estimation networks, which is applied to a black box generator model through adversarial learning and probabilistic encoder network learning. We can find the posterior distribution of the parameters for

According to the present disclosure, ALFI has been tested with various simulation models as well as a generative model using a neural network, and it can be confirmed that ALFI achieves the best parameter estimation accuracy with a limited simulation budget.

Adversarial Likelihood-Free Inference

에 대한 샘플링 기반 추론을 할 수 있다. The present disclosure relates to a black box generator and to Adversarial Likelihood-Free Inference (ALFI), a Bayesian inference that can operate in an adversarial setting. In one embodiment, the ALFI is post-mortem by the Metropolis-Hastings algorithm, assuming that it uses a neural network or other type of black box generator, such as a probabilistic simulation.

Sampling-based inference can be made about

1. Motivation for ALFI Development

로 사용하여 표준 가우시안 분포로 간주되는 이전 분포

로 데이터 분포

를 모델링한다. 여기에서 신경망 기반 생성기는

외에 확률론 (stochasticity)이 없으므로, 방해 확률(nuisance stochastic) 변수

는 원래의 GAN에 존재하지 않는다. 대신, GAN 문헌에서

를

에 매핑하도록 생성기 매개 변수

를 최적화 할 수 있다.Conventional GANs generate neural networks

Previous distribution considered to be the standard Gaussian distribution using

Raw data distribution

to model Here, the neural network-based generator is

Since there is no stochasticity other than that, the nuisance stochastic variable

does not exist in the original GAN. Instead, in the GAN literature

cast

generator parameters to map to

can be optimized.

의 확장을 가정한다. 의미있는 노이즈 잡음 변수

를 갖는 노이즈를 사용한 다양한 시뮬레이션과 같은 확률적 생성기가 있을 수 있다. 특히, 이들 블랙 박스 생성기는 일정한 모델 구조를 상수

로서 가질 수 있는데, 즉 고정 계수

와 랜덤 노이즈

를 갖는 물리적 현상을 모델링하는 확률적 시뮬레이터

이다. 이 가설은

가 입력 분포

를 유추하여

만 생성 할 수 있음을 나타낸다. 이 가설에서는

의 모양을 학습해야 하지만 GAN의

는 표준 가우스 분포로 고정되어 있기 때문에 원래 GAN과 다르다. The present disclosure

It is assumed that the expansion of Meaningful Noise Noise Variables

There may be probabilistic generators such as various simulations using noise with In particular, these black box generators have a constant model structure

can have as , that is, a fixed coefficient

and random noise

A probabilistic simulator to model a physical phenomenon with

to be. This hypothesis is

is the input distribution

by inferring

Indicates that it can only be created. In this hypothesis

We need to learn the shape of the GAN

is different from the original GAN because it is fixed with a standard Gaussian distribution.

에 의해 이전 분포를 매개 변수화하는 방법을 제공한다. 이 매개 변수화를 통해 AVO는 REINFORCE 알고리즘에 의해

를 얻을 수 있다. 사전 분포가 없으면 입력 매개 변수

를 기울기 하강 방법으로 최적화 할 수 없다. AVO가 적대적 프래임워크과 블랙 박스 모델의 공동 고려를 도입했지만, AVO는 두 가지 주요한 단점이 있다. 하나는 판별자의 최적성(optimality)이고 다른 하나는 생성기의 최적성이다. 따라서, 적대적 설정에서 베이지안 추론을 위한 새로운 방법론이 필요하다.AVO is an implicit suggestion distribution

provides a way to parameterize the previous distribution by With this parameterization, the AVO is determined by the REINFORCE algorithm

can get input parameter without prior distribution

cannot be optimized by the gradient descent method. Although AVO introduced the adversarial framework and joint consideration of the black box model, AVO has two major drawbacks. One is the optimality of the discriminator and the other is the optimality of the generator. Therefore, a new methodology for Bayesian inference in adversarial settings is needed.

2. ALFI's Reasoning Procedure

2( c ) is a diagram illustrating a network structure of ALFI according to an embodiment of the present disclosure. The network architecture of ALFI can be composed of three main components:

black box generator g:

[0, 1]Discriminant Network

[0, 1]

Probabilistic encoder networks

는 모델 입력 파라미터

의 랜덤 변수가 베타 분포를 따르는 것으로 가정되는 확률적 프로세스를 추정한다. 다시 말해,

상에서 슬라이스가 있는 대리 함수는 베타 분포이며, 확률적 엔코더 네트워크는 베타 분포 모양 매개 변수

와

에 대한 상각 추론에 의해

의 응답 곡선을 추정할 수 있다. 추정된 대리 함수는 4.3에 설명 된대로 우도 비(

)를 계산하는데 사용될 수 있다. 그런 다음 Metropolis-Hastings 알고리즘은 반복 후 고정 분포에서 다음 입력 매개 변수를 샘플링할 수 있다. 확률적 프로세스

의 응답 곡선은 최적 판별자

를 사용하여 정적 응답 곡선으로 수렴할 수 있다. Probabilistic encoder networks

is the model input parameter

Estimate a probabilistic process in which the random variable of is assumed to follow a beta distribution. In other words,

The surrogate function with slices on the top is a beta distribution, and the probabilistic encoder network has a beta distribution shape parameter.

Wow

by amortization reasoning for

The response curve of can be estimated. The estimated surrogate function is the likelihood ratio (

) can be used to calculate The Metropolis-Hastings algorithm can then sample the following input parameters from a fixed distribution after iteration. stochastic process

The response curve of the optimal discriminator

can be used to converge to a static response curve.

를 찾는 반면 ALFI의 최적의 판별기는 기본 응답 곡선

를

로 안정화한다. 이 안정화된 응답 곡선

은 정적 확률론적 프로세스이다. 판별자 최적성을 얻은 후 확률적 엔코더 네트워크는 정적 확률적 프로세스를 학습한다. 따라서 ALFI의 최적 판별자는 네트워크가 최적의 매개 변수를 찾는 데 도움이 될 수 있다. 또한 ALFI는 제안 분포를 도입하지 않고 사후 분포를 직접 추정하기 때문에 AVO의 두 번째 문제는 ALFI와 관련이 없게 된다. ALFI does not have the negative aspects of AVO. First, an AVO with an optimal discriminant interferes with the distribution of the proposed

, whereas the optimal discriminator of ALFI is the default response curve

cast

is stabilized with This stabilized response curve

is a static probabilistic process. After obtaining the discriminant optimality, the probabilistic encoder network learns a static probabilistic process. Therefore, the optimal discriminator of ALFI can help the network to find the optimal parameters. Also, because ALFI directly estimates the posterior distribution without introducing a proposed distribution, the second problem of AVO becomes irrelevant to ALFI.

3. Likelihood Ratio Approximation

)을 계산할 수 있다. In an embodiment of the present disclosure, an approximate value of the likelihood ratio (

) can be calculated.

In one embodiment, ALFI may adopt explicit assumptions about the distribution shape to obtain an approximation. As one of ordinary skill in the art is well aware, the synthetic likelihood approach can be problematic due to the bias derived from the explicit assumptions, but the explicit assumptions greatly reduce the number of required simulations. There is an advantage.

ALFI can assume a beta distribution assumption for the discriminator output. However, the output of the discriminator can be multidimensional or extend infinitely, in which case a distribution assumption other than the beta distribution may be required. Even in such cases, ALFI can provide a basic structure for inferring such a distribution.

가 고정되어 있을 때의 응답 곡선

을 1차원 확률 변수

로 생각하여, 이 확률 변수에 대한 밀도 추정을 하면 계산 불가능한 우도는 다음과 같은 확률 변수

의 밀도값으로 표현할 수 있다:

. 이 때, 우도를 밀도값으로 표현하기 위한 조건은

이다.The explicit beta assumption can make it possible to compute the tractable likelihood under the following argument. described above

Response curve when is fixed

is a one-dimensional random variable

, and if density estimation is made for this random variable, the incalculable likelihood is the following random variable

It can be expressed as a density value of:

. In this case, the condition for expressing the likelihood as a density value is

to be.

는 판별자 네트워크의 출력값이기 때문에 0에서 1 사이의 제한된 범위의 값을 갖는다. 그렇기 때문에 우리는 임의의 변환

을 생각하여, 우도 추정 문제를 일반화된 범위에서 밀도를 갖는 밀도 추정 문제로 바꿀 수 있다. 즉,

로 변환된 확률 변수

에 대하여 우도는

라고 표현할 수 있다.random variable

Since is the output value of the discriminant network, it has a limited range of values from 0 to 1. That's why we use arbitrary transformations

We can change the likelihood estimation problem to a density estimation problem with density in a generalized range. in other words,

random variable transformed into

About Udo

can be expressed as

가 밀도 함수

와 모수

를 가지는 분포를 따른다고 가정하였을 때, 우도는 다음과 같이 표현할 수 있다:

.Now, to estimate the likelihood, it is assumed that the reconstructed one-dimensional density follows a determined probability distribution, and the likelihood can be estimated by obtaining the parameters expressing the probability distribution. That is, if the probability distribution

density function

with parameters

Assuming that it follows a distribution with , the likelihood can be expressed as:

.

와 파라미터

간의 우도 비율은 아래와 같다:

.After that, the parameter

and parameters

The likelihood ratios between the two are:

.

4.4. Algorithm

ALFI can use the discriminant loss function of (Goodfellow et al., 2014).

(9)

(9)

[Algorithm 1]

에 대한 기대 값은 m회 반복 후 매트로폴리스-해스팅 알고리즘에 의해 선택된 n 개의 표본에 대해 계산되며, 여기서 m은 매트로폴리스-해스팅 알고리즘의 고정(stationary) 분포에 대한 수렴 속도를 제어하는 탐사-발산 하이퍼 파라미터(exploration-expoitation hyperparameter)이다. 신경망

가 정적 확률적 프로세스

로 수렴됨에 따라, 상기 선택된 n 개의 표본에 대한 표본 기대값은 m의 선택에 관계없이 고정 분포

로부터 n 개의 표본에 대한 편향되지 않은 기대값으로 수렴된다.

The expected value for α is computed for n samples selected by the metropolis-Hasting algorithm after m iterations, where m is the exploration- It is an exploration-expoitation hyperparameter. neural network

is a static stochastic process

As converges to , the sample expected value for the selected n samples is a fixed distribution regardless of the choice of m.

converges to the unbiased expected value for n samples.

Here Equation (2) is:

Equation (3) is as follows:

Equation (4) is as follows:

를 학습하기 위한 학습 데이터 세트

가 있다.For each iteration, the probabilistic encoder network

training data set to train

there is

5. Experiment

5.1. Exemplary embodiment

An exemplary black box model may describe the mechanism of ALFI. Below is a suggested example model:

이다. 실제 매개 변수

는 0.25이고, 결과적으로 관측 값

은 1이다. here,

to be. actual parameters

is 0.25, and consequently the observed value

is 1

주위에 집중됨을 알 수 있다. 둘째, 대리 함수(surrogate function)(파란색 선)은 반응 곡선(reponse curve)

를 추정할 수 있다. Figure 4(a) shows two points. First, an ALFI sample with a mini-batch size of 100 (blue dots) is an actual parameter

It can be seen that the focus is on the surroundings. Second, the surrogate function (blue line) is the response curve

can be estimated.

=0.001인 경우, 기준 모델인 Rejection ABC의 사후와 일치함을 보여준다. 도 4(c)는 ALFI의 메트로폴리스-해스팅알고리즘의 표본이 수용 가능한 시뮬레이션 실행 횟수 내에서 실제 매개 변수

로 수렴됨을 보여준다.Figure 4 (b) is the posterior (posterior) of the ALFI sample,

=0.001, it shows that it is consistent with the posterior model of Rejection ABC. Figure 4(c) shows the actual parameters within the acceptable number of simulation runs for a sample of ALFI's Metropolis-Hasting algorithm.

shows that it converges to

5.2. Simulation as a black box model

Considering the simulation as a black box model, we compare the performance of the following baseline non-likelihood inference algorithms:

- Rejection-ABC (Tavar´ et al., 1997)

- Monte-Carlo Markov-Chain (MCMC) ABC (Marjoram et al., 2003)

- BOLFI (Gutmann & Corander, 2016) and AVO (Louppe et al., 2019).

의 성능은 실제 파라미터

와 사후(posterior) 모드

사이의 음의 로그 유클리드 거리이다. 단일 관측값

은 잡음 변수 u로 구동되는 확률론(stochasticity) 최소화하기 위해

=

로 100개의 시뮬레이션 실행 결과의 평균이다. here,

The performance of the actual parameter

and posterior mode

is the negative log Euclidean distance between single observation

to minimize the stochasticity driven by the noise variable u

=

is the average of 100 simulation run results.

The present disclosure applies the Runge-Kutta 4-th order method (Runge-Kutta 4-th order method, Leader, 2004) to solve -Ordinary Differential Equations (ODE) and a finite difference method (Iserles, 2009) can be applied to solve a time-independent partial differential equation (PDE).

[Table 1]

에 의해 추정된다. 각 실제 매개 변수

에 대해 동일한 시뮬레이션 시간 예산으로 사후 모드

를 추정한다. Rejection ABC에서 시뮬레이션 실행의 0.1 %를 수용하도록 적응적으로

를 선택한다. 제안 된 분포

가 가우스 분포

인 AVO Gaussian에서 릴리스 된 AVO 코드를 사용한다. AVO NN은 암시적으로 제안 분포를 모델링하여 AVO의 바닐라 버전에서 가우스성 가정을 완화한다. 공정한 비교를 위해 AVO NN과 ALFI는 판별자에서 동일한 신경망 구조를 사용한다. -표 1은 - ALFI가 많은 시뮬레이션에서 기본 모델 보다 낫다는 것을 보여준다. 특히 ALFI는 시뮬레이션 입력 변수의 차원이 증가할수록 (Stokes, NPA 시뮬레이션) 기본 모델들보다 월등한 성능을 나타내는 것을 알 수 있다.Table 1 summarizes the performance of the algorithm. Performance is a set of 30 different real-world parameters randomly selected

is estimated by each actual parameter

Post-mode with the same simulation time budget for

to estimate Adaptively to accommodate 0.1% of simulation runs on Rejection ABC

select Suggested distribution

Gaussian distribution

AVO uses the AVO code released by Gaussian. AVO NN relaxes the Gaussian assumptions in the vanilla version of AVO by implicitly modeling the proposal distribution. For a fair comparison, AVO NN and ALFI use the same neural network structure in the discriminator. Table 1 shows that ALFI is better than the base model in many simulations. In particular, it can be seen that ALFI exhibits superior performance than basic models as the dimension of the simulation input variable increases (Stokes, NPA simulation).

를 베타 분포로 가정한 후, ALFI의 확률적 엔코더 네트워크를 학습함에 따라 베타 분포가 점점 비모수로 추정한 분포로 수렴하는 것을 보여준다. 세 번째 기둥은 판별자의 출력 분포를 보여준다. 네 번째 기둥은 베타 분포로 학습한 분포의 평균을 보여준다. 마지막인 다섯 번째 기둥은 학습한 베타 분포로 우도를 추정한 결과를 보여준다.5 shows how the ALFI algorithm operates as it progresses. The black dots in the three figures of the most discrepancy show that the algorithm gradually gathers at the true input variable as the algorithm progresses. Beta Estimation of the second column is a random variable

After assuming as the beta distribution, it shows that the beta distribution gradually converges to the nonparametrically estimated distribution as the ALFI probabilistic encoder network is trained. The third column shows the output distribution of the discriminator. The fourth column shows the average of the distributions learned with the beta distribution. The last column, the fifth column, shows the result of estimating the likelihood with the learned beta distribution.

Fig. 6 shows a Poisson simulation result when the observation is the same as that of Fig. 6(a). As shown, reproduction of ALFI is more consistent with observations than reproduction of AVO.

5.3. GAN generator as a black box model

와 함께 MNIST 이미지 생성기

를 사용할 수 있다. 일 실시예에서, 마스크된 이미지의 가장 가까운 잠재 삽입을 추정하여 마스크 된 이미지에서 실제 이미지를 재생산하도록 설계될 수 있다. According to an embodiment of the present disclosure, an experiment may be designed by treating the DCGAN (Radford et al., 2015) generator as a black box model. In particular, we have pre-trained fixed generator coefficients through an ALFI learning process.

with MNIST image generator

can be used In one embodiment, it may be designed to reproduce the real image from the masked image by estimating the nearest latent interpolation of the masked image.

7 is a diagram illustrating a pair of a real sample and a masked observation value of the real sample, according to an embodiment of the present disclosure.

According to the present disclosure, an ALFI or AVO NN can infer the vector input of the DCGAN generator to regenerate an image similar to the real image when the validation data set is provided with a mask and corrupted observations. 7 , ALFI can generate an image more similar to an actual image than AVO NN can generate.

6. Conclusion

We developed ALFI because of a problem with AVO. In this respect, ALFI estimates the actual parameters more accurately than AVO. ALFI's contribution lies in two different layers. The first tier of contribution is to introduce new non-likelihood inferences to black box generators in adversarial frameworks.

The second layer of contribution is the practical application of finding the best calibrated parameters given the validation data set and completing a high fidelity simulation model. It should also be noted that the utilization of black box generative models frequently occurs in the neural network community, where a few examples are presented and pre-trained fixed generators are used.

As will be appreciated by those skilled in the art, the present disclosure is not limited to the examples described herein, and various modifications, reconstructions, and substitutions may be made without departing from the scope of the present disclosure. For example, the various techniques described herein may be implemented by hardware or software, or a combination of hardware and software. Accordingly, certain aspects or portions of the analysis machine for software safety analysis according to the present disclosure may be implemented in one or more computer programs executable by a general-purpose or dedicated microprocessor, micro-controller, or the like. A computer program according to an embodiment of the present disclosure includes a storage medium readable by a computer processor or the like, such as EPROM, EEPROM, non-volatile memory such as a flash memory device, magnetic disk such as an internal hard disk and a removable disk, a magneto-optical disk, and It may be implemented in a form stored in various types of storage media including a CDROM disk and the like. In addition, the program code(s) may be implemented in assembly language or machine language, and may be implemented in a form transmitted through electric wiring, cabling, optical fiber, or any other type of transmission medium.

Although exemplary embodiments have been primarily described herein with reference to various drawings, other similar embodiments may be utilized. All modifications and variations falling within the true spirit and scope of the present disclosure are intended to be embraced by the following claims.

Claims (7)

A method for inference of adversarial non-likelihood for a black box generator, performed on a computer system, comprising:
Discriminator network:

) and a probabilistic encoder network:

)about,
(a) repeating the metropolis-Hasting algorithm m times, where m is an exploration-expoitation hyperparameter that controls the convergence rate for a stationary distribution of the metropolis-Hasting algorithm, It is the number of iterations of the metropolis-Hasting algorithm -;
(b) calculating an output value obtained by substituting input variables into a black box generation model after repeating the metropolis-Hasting algorithm m times;
(c) after calculating the output value by substituting input variables into the black box generation model,
(c-1) updating the discriminator network based on a first gradient descent technique; and
(c-2) updating the probabilistic encoder network based on a second gradient descent technique
repeating (c-1) and (c-2) l times, where l is the number of iterations of gradient descent for learning the discriminator network and the probabilistic encoder network;
An adversarial non-likelihood inference method for a black box generator comprising According to claim 1,
The step of repeating the metropolis-Hasting algorithm m times is an adversarial non-likelihood inference method for a black box generator that is calculated using the input variables of the next black box generation model. 3. The method of claim 2,
The first gradient descent method is an adversarial non-likelihood inference method for a black box generator that is trained to optimize Equation (3) below.
Formula (3):

here,

is a function for applying the gradient descent technique of the discriminant network,

is the output for the sample input extracted from the actual data distribution Pr of the discriminant network,

is the output for the sample input extracted from the generative data distribution Pg of the discriminant network. 4. The method of claim 3,
The second gradient descent method is an adversarial non-likelihood inference method for a black box generator that is learned to optimize Equation (4) below.
Formula (4):

here,

is a function for applying the gradient descent technique of the probabilistic encoder network,

is the expected value of the result when the output output from the black box generation model is input to the discriminator network using the generative model input presented in the encoder network. 5. The method of claim 4,
Equation (4) is an adversarial non-likelihood inference method for a black box generator that is learned in the direction of optimizing the likelihood to infer the random variable generated from the discriminator. An apparatus configured to provide adversarial non-likelihood inference for a black box generator, comprising:
a computing module;
The computing module is a discriminator network (discriminator network:

) and a probabilistic encoder network:

)about,
(a) iterates the metropolis-Hasting algorithm m times, where m is the exploration-expoitation hyperparameter that controls the convergence rate for the stationary distribution of the metropolis-Hasting algorithm. , the number of iterations of the Metropolis-Hasting algorithm -;
(b) after repeating the Metropolis-Hasting algorithm m times, it is configured to calculate an output value by substituting input variables into the black box generation model;
(c) After calculating the output value by substituting the input variable into the black box generation model,
(c-1) updating the discriminator network based on a first gradient descent technique;
(c-2) updating the probabilistic encoder network based on a second gradient descent technique;
configured to repeat (c-1) and (c-2) l times, where l is the number of iterations of gradient descent for learning the discriminator network and the probabilistic encoder network;
Adversarial non-likelihood inference device for black box generator. A computer-readable recording medium containing one or more computer-readable instructions executable by a computer, wherein the one or more computer-readable instructions, when executed by the computer, cause the computer to: A computer-readable recording medium for performing the method according to any one of the preceding claims.

Images