Discrete latent variables. has several applications Stochastic Optimization w.

Discrete latent variables. The standalone Mar 20, 2024 · Discrete latent variables represent a choice or category from a finite set. Most studies focus on the linear latent variable model or impose strict constraints on latent structures, which fail to address cases in discrete data involving non-linear relationships or complex latent Furthermore, discrete representations are a natural fit for complex reasoning, planning and predictive learning (e. The approach … A latent variable model, as the name suggests, is a statistical model that contains latent, that is, unobserved, variables. e. io Sep 7, 2016 · Probabilistic models with discrete latent variables naturally capture datasets composed of discrete classes. It allows us to formulate interpretable and flexible models that can be used to analyze complex datasets in the presence of articulated dependence structures among variables. With this accessible tool, the application of data modeling with discrete latent variables becomes feasible for a broad range of empirical studies. 0. Sep 26, 2019 · The discrete latent variables \ (z\) are then calculated by a nearest neighbor look-up using the shared embedding space \ (e\): This forward computation pipeline can be seen as a regular autoencoder with a particular non-linearity that maps the latents to 1-of-\ (K\) embedding vectors. To this end, we build a topic-aware latent code-guided text generation model. Section 9. In this paper, we develop a topic-informed discrete latent variable model for semantic textual Dec 1, 2012 · This paper describes and applies a general approach for incorporating factors with structural equations into models for discrete choice. In RL, C represents the size of the discrete action space and z is a sequence of discrete actions from that space. However in many applications, sparse representations are expected, such as learning sparse high dimensional embedding of data in an Abstract Despite recent improvements in training methodology, discrete latent variable models have failed to achieve the performance and popularity of their continuous counterparts. Intended Learning Outcomes ¶ After this tutorial the student should be able to parameterise a latent variable model with discrete latent variables estimate parameters using exact log-likelihood function (when tractable) estimate parameters using neural variational inference Latent variables pose a challenge for accurate modelling, experimental design, and inference, since they may cause non-adjustable bias in the estimation of effects. We consider sev-eral approaches to learning discrete latent vari-able models for text in the case where ex-act marginalization over these variables is in-tractable. 本文未经允许禁止转载，谢谢合作。作者：Light Sea@知乎本文介绍Deepmind的工作VQ-VAE，一种使用了discrete latent variables的VAE。我们之前已经介绍了使用 continuous latent variables的VAE，然而一些类型的数… Nov 7, 2022 · Recently, discrete latent variable models have received a surge of interest in both Natural Language Processing (NLP) and Computer Vision (CV), attributed to their comparable performance to the continuous counterparts in representation learning, while being more interpretable in their predictions. Generally, approaches have relied on control variates to reduce the variance of the REINFORCE estimator. Most studies focus on the linear latent variable model or impose strict constraints on latent structures, which fail to address cases in discrete data involving non-linear relationships or complex latent structures. Oct 27, 2025 · A natural text always revolves around several related topics and the transition across them is natural and smooth. [2] Common use cases for latent variable models include applications in psychometrics (e. , given an image x what are the latent factors z, then once we find some image with missing parts, the latent factors can be used for reconstruction. Given the measurement model, the causal structure over the latent variable is identified up to a Markov equivalent class by the PC-TENSOR-RANK algorithm. Here we address Jan 10, 2024 · We propose an evolutionary optimization method for maximum likelihood and approximate maximum likelihood estimation of discrete latent variable models. Conventional methods obtain a differentiable estimate of the ELBO with reparametrized sampling and optimize it with Stochastic Gradient Descend This paper introduces Vector Quantised-Variational AutoEncoder (VQ-VAE), a model for learning discrete representations without supervision in machine learning. Training models with discrete latent variables is challenging due to the high variance of unbiased gradient estimators. Specific models including discrete latent variables are illustrated, such as finite mixture, latent class, hidden Jul 23, 2025 · Categorical Latent Variables: These are unobservable variables that represent discrete categories or groups. Active learning seeks to reduce the amount of data required to fit the parameters of a model, thus forming an important class of techniques in modern machine learning. Here, we evaluate several approaches to training large-scale image models on CIFAR-10 using a probabilistic variant of the recently proposed Vector Quantized VAE architecture. May 30, 2020 · If we can do a posterior inference on the latent variables i. However Oct 27, 2025 · We also introduce discrete latent variables to tackle the inherent one-to-many mapping problem in response generation. Latent variable models are applied across a wide range of fields such as biology, computer science, and social science. We intro-duce a novel class of probabilistic models, comprising an undirected discrete com-ponent and a directed hierarchical continuous component Nov 8, 2016 · In this post, I discuss our recent paper, Categorical Reparameterization with Gumbel-Softmax, which introduces a simple technique for training neural networks with discrete latent variables. has several applications Stochastic Optimization w. We present a novel method to train a class of probabilistic models with discrete latent variables using the variational autoencoder framework, including Oct 13, 2025 · Explore what latent variable modeling is, how it can benefit you, and how to choose the right model based on your research question and data types. However, past work on active learning has largely overlooked latent variable models, which play a vital role in neuroscience, psychology, and a variety of other engineering and scientific disciplines. Discover how latent variables can be used to build sophisticated models capable of capturing complex hidden non linear relationships in data (automatic feature extraction). github. We show that compared with the Straight-Through estimator, the Gumbel-Softmax relaxation provides a better solution to learn hash codes and thus gains the state of the art performance in three different datasets. This allows relatively complex marginal distributions over observed variables to be ex-pressed in terms of more tractable joint distributions over the expanded space of observed and latent variables. Summary Pyro implements automatic enumeration over discrete latent variables. A latent variable model is a statistical model that relates set of observable variables (also called manifest variables or indicators) [1] to a set of latent variables. Summary Discovering discrete latent structure e. Recent work (Jang et al. However, they are difficult to train efficiently, since backpropagation through discrete variables is generally not possible. Jun 1, 2022 · We propose a model based on discrete latent variables, which are spatially associated and time specific, for the analysis of incident cases of SARS-Co… Mar 21, 2017 · Learning in models with discrete latent variables is challenging due to high variance gradient estimators. To Feb 16, 2024 · Abstract. While low-variance reparameterization gradients of a continuous relaxation can provide an effective solution, a continuous relaxation is not always available or tractable. The pur-pose of this article is to offer a framework of discrete latent variable models for data analysis, and to develop the MDLV toolbox for use in estimating each model under this frame-work. We review the discrete latent variable approach, which is very popular in statistics and related fields. t. Jul 23, 2025 · Categorical Latent Variables: These are unobservable variables that represent discrete categories or groups. Nov 22, 2018 · I am creating a Bayesian Network where all nodes are discrete. We present a method to extend sequence models using discrete latent variables that makes decoding much more parallel. Standard VAEs assume continuous-valued latent variables and are trained by maximization of the evidence lower bound (ELBO). Unlike continuous variables, which can represent a smooth spectrum of values, discrete variables categorize inputs into A Discrete Variational Lower Bound Recall that for GMM we computed marginal likelihood by explicitly marginalizing over the latent variable: This leads to fewer parameters (more latent variables will not demand more parameters) and has a potentially useful by-product: an inference model, that is, a model of the distribution of the latent variable. In this work, we investigate whether discrete latent codes can learn information of topics. g. . Their roots go back to Spearman's 1904 seminal work [1] on factor analysis, which is arguably the first well-articulated latent variable model to be widely used in psychology, mental health research, and allied disciplines. The main idea behind this approach is to first autoencode the target sequence into a shorter discrete latent sequence, which is generated autoregressively, and finally decode the full sequence from this shorter latent sequence Abstract Probabilistic models with discrete latent variables naturally capture datasets com-posed of discrete classes. Because of the association of factor analysis In dis-crete latent variable models, K will be the dimension of the discrete latent space, each dimension of which can be further represented as a C-dimensional one-hot vector. parameterized discrete distributions is challenging The log derivative trick is the general purpose technique for gradient estimation, but sufers from high variance Control variates can help in controlling the variance Continuous relaxations to Structural equation mixture modeling (SEMM) integrates continuous and discrete latent variable models. r. 1 This chapter shows how to code several widely-used models involving latent discrete parameters. The data representations learned with the models are often continuous and dense. 2 ~ Assumption 2. See full list on deepgenerativemodels. parameterized discrete distributions is challenging The log derivative trick is the general purpose technique for gradient estimation, but sufers from high variance Control variates can help in controlling the variance Continuous relaxations to Mar 20, 2024 · Discrete latent variables represent a choice or category from a finite set. We augment DMs with learnable discrete latents, inferred with an encoder, and train DM and encoder end-to-end. For instance, a person's mood (happy, sad, neutral) or personality type (introvert, extrovert) can be treated as categorical latent variables. Unlike continuous variables, which can represent a smooth spectrum of values, discrete variables categorize inputs into Summary Discovering discrete latent structure e. Abstract While much work on deep latent variable models of text uses continuous latent vari-ables, discrete latent variables are interesting because they are more interpretable and typi-cally more space efficient. , if it rains, I will use an umbrella). Apr 3, 2023 · Deep latent generative models have attracted increasing attention due to the capacity of combining the strengths of deep learning and probabilistic models in an elegant way. Two reciprocal tasks of response generation and latent act recognition are designed and carried out simultaneously within a shared network. We find that biased estimators such as The Variational Autoencoder (VAE) is a popular generative latent variable model that is often used for representation learning. While using discrete latent variables in deep learning has proven challenging, powerful autoregressive models have been developed for modelling distributions over discrete variables [37]. This tutorial assumes the reader is already familiar with the Tensor Shapes Tutorial. In the discrete 3PLSM, suppose Assumption 2. 4 hold. Abstract: Unobserved discrete data are ubiquitous in many scientific disciplines, and how to learn the causal structure of these latent variables is crucial for uncovering data patterns. Jun 11, 2024 · Unobserved discrete data are ubiquitous in many scientific disciplines, and how to learn the causal structure of these latent variables is crucial for uncovering data patterns. We compare the LATENT VARIABLES: TRUTH, LIES, AND EVERYTHING BETWEEN Karen Bandeen-Roche Department of Biostatistics Johns Hopkins University In this paper, we present a generative model with discrete latent variables to learn binary representa-tion for semantic hashing. , summarizing We propose Discrete-Continuous Latent Variable Diffusion Models (DisCo-Diff) to simplify this task by introducing complementary discrete latent variables. 1 If we define a joint distribution over observed and latent variables, the correspond-ing distribution of the observed variables alone is obtained by marginalization. 2016, Maddison et al. , categories, rankings, matchings etc. Of particular interest are discrete latent variables, which can recover categorical and structured encodings of hidden aspects of the data, leading to compact representations and, in some cases, superior explanatory power [4, 5]. Infomax learning for latent variable models thus ofers a powerful for characterizing temporally structured latent states, with a wide variety of applications in neuroscience and beyond. While most of the research regarding latent variables revolves around accounting for their presence and learning how they interact with other variables in the experiment, their bare existence is assumed to be deduced based on We first auto-encode the target sequence into a shorter sequence of discrete latent variables, which at inference time is generated autoregressively, and finally de-code the output sequence from this shorter latent sequence in parallel. We consider several approaches to learning discrete latent variable models for text in the case where exact marginalization over these variables is intractable. To discuss and develop a realistic LVM, we will formulate Gaussian Mixture Model (GMM) in terms of discrete latent variables. The proposal is based on modified versions of the expectation–maximization (EM) and variational EM (VEM) algorithms, which are based on the genetic approach and allow us to accurately explore the parameter space, reducing the chance to be Mar 9, 2018 · To this end, we introduce a novel method for constructing a sequence of discrete latent variables and compare it with previously introduced methods. Specific models including discrete latent variables are illustrated, such as finite mixture, latent class, hidden Jun 11, 2020 · While much work on deep latent variable models of text uses continuous latent variables, discrete latent variables are interesting because they are more interpretable and typically more space efficient. Drawing on prior research on the relationships between continuous and discrete latent variable models, the authors identify 3 conditions that may lead to the estimation of spurious latent classes in SEMM: misspecifica-tion of the structural model, nonnormal continuous measures, and nonlinear Most studies focus on the linear latent variable model or impose strict constraints on latent structures, which fail to address cases in discrete data involving non-linear relationships or complex latent structures. Inference with Discrete Latent Variables This tutorial describes Pyro’s enumeration strategy for discrete latent variable models. Using the available data, I have learned the structure of the network using the Hill-Climb algorithm (hc() function in bnlearn package Structural equation mixture modeling (SEMM) integrates continuous and discrete latent variable models. We compare the performance of 1 Introduction Neural latent variable models are powerful and expressive tools for finding patterns in high-dimensional data, such as images or text [1–3]. We compare the performance of the learned representations as features for low-resource document and sentence classification. 2016) has taken a different approach, introducing a continuous relaxation of discrete variables to produce low-variance, but biased Nevertheless, it is possible to code many models that involve bounded discrete parameters by marginalizing out the discrete parameters. This strategy can be used alone or inside SVI (via TraceEnum_ELBO), HMC, or NUTS. Drawing on prior research on the relationships between continuous and discrete latent variable models, the authors identify 3 conditions that may lead to the estimation of spurious latent classes in SEMM: misspecifica-tion of the structural model, nonnormal continuous measures, and nonlinear We review the discrete latent variable approach, which is very popular in statistics and related fields. Finally, we evaluate our model end-to-end on the task of neural machine translation, where it is an order of magnitude faster at decoding than comparable autoregressive models. The introduction Nov 2, 2023 · Discrete Latent Variables Chapter First Online: 02 November 2023 pp 459–493 Cite this chapter Download book PDF Jun 5, 2025 · Most studies focus on the linear latent variable model or impose strict constraints on latent structures, which fail to address cases in discrete data involving non-linear relationships or complex latent structures. The latent variable models we have considered so far are based on a map-ping from latent variables to data variables of the form (6) in which the function y(x; w) is linear in x. jearp 22spd w5z50 chkcx 4ueegz xfy vzdi zaqe lh bkplats

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