Counterfactual Identification and Latent Space Enumeration in Discrete Outcome Models

Extracting latent nonlinear dynamics from observed time-series data is important for understanding a dynamic system against the background of the observed data. A state space model is a probabilistic graphical model for time-series data, which describes the probabilistic dependence between latent variables at subsequent times and between latent variables and observations. Since, in many situations, the values of the parameters in the state space model are unknown, estimating the parameters from observations is an important task. The particle marginal Metropolis–Hastings (PMMH) method is a method for estimating the marginal posterior distribution of parameters obtained by marginalization over the distribution of latent variables in the state space model. Although, in principle, we can estimate the marginal posterior distribution of parameters by iterating this method infinitely, the estimated result depends on the initial values for a finite number of times in practice. In this paper, we propose a replica exchange particle marginal Metropolis–Hastings (REPMMH) method as a method to improve this problem by combining the PMMH method with the replica exchange method. By using the proposed method, we simultaneously realize a global search at a high temperature and a local fine search at a low temperature. We evaluate the proposed method using simulated data obtained from the Izhikevich neuron model and Lévy-driven stochastic volatility model, and we show that the proposed REPMMH method improves the problem of the initial value dependence in the PMMH method, and realizes efficient sampling of parameters in the state space models compared with existing methods.

This article presents a novel data-driven approach to nonlinear system control using a behavioral systems framework. A dynamic latent variable autoencoder (DLVAE) is proposed to project the nonlinear physical variable space onto a linear latent variable space. A data-predictive control approach is developed to control the physical process variables through the latent variables. Based on the behavioral systems theory, the proposed data-driven control framework does not require knowledge of the causality of the latent variables. The stability of the controlled system is ensured by utilizing the concept of trajectory-based dissipativity. The robustness of this control approach is achieved by incorporating the Lipschitz bounds between the latent and physical variables under dissipativity conditions.

We propose a framework for analyzing the sensitivity of counterfactuals to parametric assumptions about the distribution of latent variables in structural models. In particular, we derive bounds on counterfactuals as the distribution of latent variables spans nonparametric neighborhoods of a given parametric specification while other “structural” features of the model are maintained. Our approach recasts the infinite‐dimensional problem of optimizing the counterfactual with respect to the distribution of latent variables (subject to model constraints) as a finite‐dimensional convex program. We also develop an MPEC version of our method to further simplify computation in models with endogenous parameters (e.g., value functions) defined by equilibrium constraints. We propose plug‐in estimators of the bounds and two methods for inference. We also show that our bounds converge to the sharp nonparametric bounds on counterfactuals as the neighborhood size becomes large. To illustrate the broad applicability of our procedure, we present empirical applications to matching models with transferable utility and dynamic discrete choice models.

This work presents the solution based on the augmenting sequence of linear programming problems (LPP) as a tool for intellectualizing home environment. The proposed solution empowers the intelligent decision making procedure which can be applied to various intelligent control applications. The augmenting self-training procedure based on LPP approach is presented as well, which allows making reasonable decisions having only limited data about the controlled environment. The method permits retraining the decision making system when new data is available. As a proof of concept, this solution is applied to intelligent light control application. The obtained simulation results show the method’s capability in making reasonable decisions according to users preferences. DOI: http://dx.doi.org/10.5755/j01.itc.44.2.10235

In recent years, advancements in artificial intelligence, especially in natural language processing (NLP) models, have progressed rapidly. These models demonstrate remarkable results through training on large datasets and extensive architectures. However, the output process is often a black box, and the decision-making process remains unclear. Our research focuses on the internal representations, specifically the latent variables, generated by NLP models. In earlier work, we explored the latent variables and spaces produced by Sentence-BERT using image generation models. This approach aimed to visualize these spaces by converting discrete textual embeddings into images, introducing continuity and revealing novel relationships. This paper presents the development of an image generation model that uses a common decoder for both GPT-2 and Sentence-BERT, aimed at examining how differences in model architecture affect their latent spaces. We also investigate the impact of training dataset differences by comparing models trained in English and Japanese. Our findings indicate that while the models often generate similar outputs, significant differences emerge in sentences containing multiple elements, attributable to the differing focuses and objectives of the models. Our goal is to understand these latent spaces and contribute to the development of explainable AI.

<p><strong>Deep generative models have greatly advanced the field of artificial intelligence by learning the distribution of unlabelled datasets. In this thesis, we aim to develop a novel variational autoencoder (VAE)-based deep generative model that learns meaningful representations for effective unsupervised clustering in the latent space of high-dimensional datasets.</strong></p><p>Existing VAE-based deep clustering algorithms assume a mixture distribution either for the variational posterior over the latent variables or for the prior, to approximate the distribution of unlabelled datasets. The proposed mixtures variational autoencoders (MVAE) model assumes a mixture distribution for both the prior and variational posterior over the latent variables within the VAE framework.</p><p>We apply the variational inference to construct the evidence lower bound (ELBO) of the marginal log-likelihood function for our proposed MVAE model and then derive the analytical form for the clustering assignment estimate, also called the posterior probability estimate. This estimate is associated with each component of the VAE framework and enables the optimization of two distinct ELBO functions based on soft and hard assignment approaches. The training procedure for MVAE involves the joint optimization of both clustering assignment probabilities and model parameters. We evaluate the clustering performance on the latent embeddings of a dataset using both the posterior probability estimate and the Gaussian mixture model (GMM) methods.</p><p>We proposed two variants of the expectation-maximization (EM) algorithm to optimize the parameters for the MVAE model. The MVAE (EM) algorithm provides two distinct, numerically stable solutions for the posterior probability estimate: MVAE(EM-V1), where the estimate is associated with only the prior distribution, and MVAE(EM-V2), where the estimate incorporates both the variational posterior and the prior distribution. Among the proposed models, MVAE(EM-V2) requires less computation time for training. Additionally, this model achieves superior clustering performance on most datasets compared to the baseline models.</p><p>We modified the MVAE(EM-V2) algorithm by including a coefficient (β) with the regularizer term. The trained regularized mixtures VAE model with a small regularization coefficient (β < 1) achieves good unsupervised clustering performance on the test datasets. We further propose a variant of the regularized mixtures VAE model in which the regularization coefficient follows an annealing schedule from β > 1 to β < 1. The scheduled regularized model demonstrates superior clustering accuracy across most benchmark datasets compared to state-of-the-art deep clustering algorithms.</p><p>In this thesis, we point out that assuming a mixture distribution for both the prior and variational posterior components over the latent variables within the VAE framework enhances unsupervised clustering in the latent space. Our proposed models outperform state-of-the-art deep clustering algorithms, including VADE and k-DVAE, as well as the standard VAE model, in cluster analysis of latent representations across most benchmark datasets. Additionally, the proposed models demonstrate reasonable reconstruction performance and generate realistic examples from the latent space.</p>

Dimension reduction on neural activity paves a way for unsupervised neural decoding by dissociating the measurement of internal neural state repetition from the measurement of external variable tuning. With assumptions only on the smoothness of latent dynamics and of internal tuning curves, the Poisson Gaussian-process latent variable model (P-GPLVM) (Wu et al., 2017) is a powerful tool to discover the low-dimensional latent structure for high-dimensional spike trains. However, when given novel neural data, the original model lacks a method to infer their latent trajectories in the learned latent space, limiting its ability for estimating the internal state repetition. Here, we extend the P-GPLVM to enable the latent variable inference of new data constrained by previously learned smoothness and mapping information. We also describe a principled approach for the constrained latent variable inference for temporally-compressed patterns of activity, such as those found in population burst events (PBEs) during hippocampal sharp-wave ripples, as well as metrics for assessing whether the inferred new latent variables are congruent with a previously learned manifold in the latent space. Applying these approaches to hippocampal ensemble recordings during active maze exploration, we replicate the result that P-GPLVM learns a latent space encoding the animal’s position. We further demonstrate that this latent space can differentiate one maze context from another. By inferring the latent variables of new neural data during running, certain internal neural states are observed to repeat, which is in accordance with the similarity of experiences encoded by its nearby neural trajectories in the training data manifold. Finally, repetition of internal neural states can be estimated for neural activity during PBEs as well, allowing the identification for replay events of versatile behaviors and more general experiences. Thus, our extension of the P-GPLVM framework for unsupervised analysis of neural activity can be used to answer critical questions related to scientific discovery.

Generative models rely on the idea that data can be represented in terms of latent variables which are uncorrelated by definition. Lack of correlation among the latent variable support is important because it suggests that the latent-space manifold is simpler to understand and manipulate than the real-space representation. Many types of generative model are used in deep learning, e.g., variational autoencoders (VAEs) and generative adversarial networks (GANs). Based on the idea that the latent space behaves like a vector space Radford et al. (2015), we ask whether we can expand the latent space representation of our data elements in terms of an orthonormal basis set. Here we propose a method to build a set of linearly independent vectors in the latent space of a trained GAN, which we call quasi-eigenvectors. These quasi-eigenvectors have two key properties: i) They span the latent space, ii) A set of these quasi-eigenvectors map to each of the labeled features one-to-one. We show that in the case of the MNIST image data set, while the number of dimensions in latent space is large by design, 98% of the data in real space map to a sub-domain of latent space of dimensionality equal to the number of labels. We then show how the quasi-eigenvectors can be used for Latent Spectral Decomposition (LSD). We apply LSD to denoise MNIST images. Finally, using the quasi-eigenvectors, we construct rotation matrices in latent space which map to feature transformations in real space. Overall, from quasi-eigenvectors we gain insight regarding the latent space topology.

The smearing estimate is proposed as a nonparametric estimate of the expected response on the untransformed scale after fitting a linear regression model on a transformed scale. The estimate is consistent under mild regularity conditions, and usually attains high efficiency relative to parametric estimates. It can be viewed as a low-premium insurance policy against departures from parametric distributional assumptions. A real-world example of predicting medical expenditures shows that the smearing estimate can outperform parametric estimates even when the parametric assumption is nearly satisfied.

In this paper, a branch and bound approach is proposed for global optimization problem (P) of the sum of generalized polynomial fractional functions under generalized polynomial constraints, which arises in various practical problems. Due to its intrinsic difficulty, less work has been devoted to globally solving this problem. By utilizing an equivalent problem and some linear underestimating approximations, a linear relaxation programming problem of the equivalent form is obtained. Consequently, the initial non-convex nonlinear problem (P) is reduced to a sequence of linear programming problems through successively refining the feasible region of linear relaxation problem. The proposed algorithm is convergent to the global minimum of the primal problem by means of the solutions to a series of linear programming problems. Numerical results show that the proposed algorithm is feasible and can successfully be used to solve the present problem (P).

The use of iterative linear programming in practical applications of animal diet formulation

Many failure root cause analysis (RCA) algorithms for microservices have been proposed with the widespread adoption of microservices systems. Existing algorithms generally focus on RCA with ranking single-level (e.g. metric-level or service-level) root cause candidates (RCCs) with comprehensive monitoring metrics. However, many heterogeneous RCCs exist with limited observability in real-world microservices systems. Further, we find that the limited observability may result in inaccurate RCA through real-world failures in eBay. In this paper, for the first time, we propose to "model RCCs as latent variables". The core idea is to infer the status of RCCs as latent variables with related monitoring metrics instead of directly extracting features from only the observable metrics. Based on this, we propose LatentScope, an unsupervised RCA framework with heterogeneous RCCs under limited observability. A dual-space graph is proposed to model both observable and unobservable variables, with many-to-many relationships between spaces. To achieve fast inference of latent variables and RCA, we propose the LatentRegressor algorithm, which includes Regression-based Latent-space Intervention Recognition (RLIR) to achieve intervention recognition-based RCA in latent space. LatentScope has been deployed in eBay's production environment and evaluated on both eBay's real-world failures and a testbed dataset. The evaluation results show that, compared with baseline algorithms, our model significantly improves the Top-1 recall by 9.7%-57.9%. The source code of LatentScope and the dataset are available at https://github.com/NetManAIOps/LatentScope.

Asymmetric deep generative models

Deep directed generative models have attracted much attention recently due to their generative modeling nature and powerful data representation ability. In this article, we review different structures of deep directed generative models and the learning and inference algorithms associated with the structures. We focus on a specific structure that consists of layers of Bayesian networks (BNs) due to the property of capturing inherent and rich dependencies among latent variables. The major difficulty of learning and inference with deep directed models with many latent variables is the intractable inference due to the dependencies among the latent variables and the exponential number of latent variable configurations. Current solutions use variational methods, often through an auxiliary network, to approximate the posterior probability inference. In contrast, inference can also be performed directly without using any auxiliary network to maximally preserve the dependencies among the latent variables. Specifically, by exploiting the sparse representation with the latent space, max-max instead of maxsum operation can be used to overcome the exponential number of latent configurations. Furthermore, the max-max operation and augmented coordinate ascent (AugCA) are applied to both supervised and unsupervised learning as well as to various inference. Quantitative evaluations on benchmark data sets of different models are given for both data representation and feature-learning tasks.

Distance sampling and capture–recapture are the two most widely used wildlife abundance estimation methods. capture–recapture methods have only recently incorporated models for spatial distribution and there is an increasing tendency for distance sampling methods to incorporated spatial models rather than to rely on partly design-based spatial inference. In this overview we show how spatial models are central to modern distance sampling and that spatial capture–recapture models arise as an extension of distance sampling methods. Depending on the type of data recorded, they can be viewed as particular kinds of hierarchical binary regression, Poisson regression, survival or time-to-event models, with individuals’ locations as latent variables and a spatial model as the latent variable distribution. Incorporation of spatial models in these two methods provides new opportunities for drawing explicitly spatial inferences. Areas of likely future development include more sophisticated spatial and spatio-temporal modelling of individuals’ locations and movements, new methods for integrating spatial capture–recapture and other kinds of ecological survey data, and methods for dealing with the recapture uncertainty that often arise when “capture” consists of detection by a remote device like a camera trap or microphone.