Understanding the Distillation Process from Deep Generative Models to Tractable Probabilistic Circuits
Tsinghua University（清华大学）；University of California, Los Angeles（加州大学洛杉矶分校）；Peking University（北京大学）；Beijing Institute for General Artificial Intelligence（北京通用人工智能研究院）
Xuejie Liu, Anji Liu, Guy Van den Broeck, Yitao Liang
Probabilistic Circuits (PCs) are a general and unified computational framework for tractable probabilistic models that support efficient computation of various inference tasks (e.g., computing marginal probabilities). Towards enabling such reasoning capabilities in complex real-world tasks, Liu et al. (2022) propose to distill knowledge (through latent variable assignments) from less tractable but more expressive deep generative models. However, it is still unclear what factors make this distillation work well. In this paper, we theoretically and empirically discover that the performance of a PC can exceed that of its teacher model. Therefore, instead of performing distillation from the most expressive deep generative model, we study what properties the teacher model and the PC should have in order to achieve good distillation performance. This leads to a generic algorithmic improvement as well as other data-type-specific ones over the existing latent variable distillation pipeline. Empirically, we outperform SoTA TPMs by a large margin on challenging image modeling benchmarks. In particular, on ImageNet32, PCs achieve 4.06 bits-per-dimension, which is only 0.34 behind variational diffusion models (Kingma et al., 2021).
TU Darmstadt（达姆施塔特工业大学）；The University of Texas at Dallas（德克萨斯大学达拉斯分校）；Hessian Center for AI (hessian.AI)（黑森人工智能中心 (hessian.AI)）
While probabilistic models are an important tool for studying causality, doing so suffers from the intractability of inference. As a step towards tractable causal models, we consider the problem of learning interventional distributions using sum-product networks (SPNs) that are over-parameterized by gate functions, e.g., neural networks. Providing an arbitrarily intervened causal graph as input, effectively subsuming Pearl's do-operator, the gate function predicts the parameters of the SPN. The resulting interventional SPNs are motivated and illustrated by a structural causal model themed arou…
Tsinghua University（清华大学）；University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
Computing the expectation of kernel functions is a ubiquitous task in machine learning, with applications from classical support vector machines to exploiting kernel embeddings of distributions in probabilistic modeling, statistical inference, causal discovery, and deep learning. In all these scenarios, we tend to resort to Monte Carlo estimates as expectations of kernels are intractable in general. In this work, we characterize the conditions under which we can compute expected kernels exactly and efficiently, by leveraging recent advances in probabilistic circuit representations. We first co…
Probabilistic circuits (PCs) are a tractable representation of probability distributions allowing for exact and efficient computation of likelihoods and marginals. There has been significant recent progress on improving the scale and expressiveness of PCs. However, PC training performance plateaus as model size increases. We discover that most capacity in existing large PC structures is wasted: fully-connected parameter layers are only sparsely used. We propose two operations: pruning and growing, that exploit the sparsity of PC structures. Specifically, the pruning operation removes unimporta…
Efficient probabilistic surrogate modeling techniques for partially-observed large-scale dynamical systems
University of Paderborn（帕德博恩大学）；Lamarr Institute for Machine Learning and Artificial Intelligence（拉马尔机器学习和人工智能研究所）；University of Michigan（密歇根大学）；Technical University of Munich（慕尼黑工业大学）；Technical University of Dortmund（多特蒙德工业大学）
Stochastic Transition-Map Distillation for Fast Probabilistic Inference
Department of Aerospace Engineering, Georgia Institute of Technology（佐治亚理工学院航空航天工程系）；Department of Computer Science, Georgia Institute of Technology（佐治亚理工学院计算机科学系）；Department of Mathematics, Florida State University（佛罗里达州立大学数学系）
Closed-Loop Unsupervised Representation Disentanglement with $β$-VAE Distillation and Diffusion Probabilistic Feedback
Ningbo Institute of Digital Twin, Eastern Institute of Technology（宁波数字孪生研究所、东部技术研究所）；Shanghai Jiao Tong University（上海交通大学）；Xi’an Jiaotong University（西安交通大学）
Skolkovo Institute of Science and Technology（斯克尔克沃科学与技术学院）；Yandex Research（Yandex研究）；HSE University（俄罗斯高等经济大学）；Artificial Intelligence Research Institute（人工智能研究 institute）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）
Tractable Representation Learning with Probabilistic Circuits
Technische Universität Darmstadt（达姆施塔特工业大学）；University of Texas, Dallas（德克萨斯大学达拉斯分校）；University of Edinburgh（爱丁堡大学）；Universität Bremen（不来梅大学）；University of Texas at Dallas（德克萨斯大学达拉斯分校）
School of Artificial Intelligence, Beijing University of Posts and Telecommunications（北京邮电大学人工智能学院）；School of Electrical and Data Engineering, University of Technology Sydney（悉尼科技大学电气与数据工程学院）
Channel attention mechanisms have been commonly applied in many visual tasks for effective performance improvement. It is able to reinforce the informative channels as well as to suppress the useless channels. Recently, different channel attention modules have been proposed and implemented in various ways. Generally speaking, they are mainly based on convolution and pooling operations. In this paper, we propose Gaussian process embedded channel attention (GPCA) module and further interpret the channel attention schemes in a probabilistic way. The GPCA module intends to model the correlations a…
Counterfactual examples are an appealing class of post-hoc explanations for machine learning models. Given input $x$ of class $y_1$, its counterfactual is a contrastive example $x^\prime$ of another class $y_0$. Current approaches primarily solve this task by a complex optimization: define an objective function based on the loss of the counterfactual outcome $y_0$ with hard or soft constraints, then optimize this function as a black-box. This "deep learning" approach, however, is rather slow, sometimes tricky, and may result in unrealistic counterfactual examples. In this work, we propose a no…
Probabilistic models learned as density estimators can be exploited in representation learning beside being toolboxes used to answer inference queries only. However, how to extract useful representations highly depends on the particular model involved. We argue that tractable inference, i.e. inference that can be computed in polynomial time, can enable general schemes to extract features from black box models. We plan to investigate how Tractable Probabilistic Models (TPMs) can be exploited to generate embeddings by random query evaluations. We devise two experimental designs to assess and com…
Argonne National Laboratory（阿贡国家实验室）；The University of Texas at Dallas（德克萨斯大学达拉斯分校）
Wind farm design primarily depends on the variability of the wind turbine wake flows to the atmospheric wind conditions, and the interaction between wakes. Physics-based models that capture the wake flow-field with high-fidelity are computationally very expensive to perform layout optimization of wind farms, and, thus, data-driven reduced order models can represent an efficient alternative for simulating wind farms. In this work, we use real-world light detection and ranging (LiDAR) measurements of wind-turbine wakes to construct predictive surrogate models using machine learning. Specifically…
University of California Los Angeles（加州大学洛杉矶分校）；Washington University in St. Louis（圣路易斯华盛顿大学）
Generating functions, which are widely used in combinatorics and probability theory, encode function values into the coefficients of a polynomial. In this paper, we explore their use as a tractable probabilistic model, and propose probabilistic generating circuits (PGCs) for their efficient representation. PGCs are strictly more expressive efficient than many existing tractable probabilistic models, including determinantal point processes (DPPs), probabilistic circuits (PCs) such as sum-product networks, and tractable graphical models. We contend that PGCs are not just a theoretical framework …
University of Edinburgh（爱丁堡大学）；Alan Turing Institute（艾伦图灵研究所）；University of Edinburgh & Alan Turing Institute（爱丁堡大学和艾伦图灵研究所（此处为合并表述，按原文提取））
Incorporating constraints is a major concern in probabilistic machine learning. A wide variety of problems require predictions to be integrated with reasoning about constraints, from modelling routes on maps to approving loan predictions. In the former, we may require the prediction model to respect the presence of physical paths between the nodes on the map, and in the latter, we may require that the prediction model respect fairness constraints that ensure that outcomes are not subject to bias. Broadly speaking, constraints may be probabilistic, logical or causal, but the overarching challen…
Enhancing Knowledge Graph Completion with GNN Distillation and Probabilistic Interaction Modeling
Shandong Key Laboratory of Industrial Network Security（山东工业网络安全重点实验室）；School of Computer Science and Technology, Harbin Institute of Technology（哈尔滨工业大学计算机科学与技术学院）
University of Oxford（牛津大学）；University of Edinburgh（爱丁堡大学）；Alan Turing Institute（艾伦·图灵研究所）
Moral responsibility is a major concern in autonomous systems, with applications ranging from self-driving cars to kidney exchanges. Although there have been recent attempts to formalise responsibility and blame, among similar notions, the problem of learning within these formalisms has been unaddressed. From the viewpoint of such systems, the urgent questions are: (a) How can models of moral scenarios and blameworthiness be extracted and learnt automatically from data? (b) How can judgements be computed effectively and efficiently, given the split-second decision points faced by some systems?…
We consider the problem of explaining a class of tractable deep probabilistic models, the Sum-Product Networks (SPNs) and present an algorithm ExSPN to generate explanations. To this effect, we define the notion of a context-specific independence tree(CSI-tree) and present an iterative algorithm that converts an SPN to a CSI-tree. The resulting CSI-tree is both interpretable and explainable to the domain expert. We achieve this by extracting the conditional independencies encoded by the SPN and approximating the local context specified by the structure of the SPN. Our extensive empirical evalu…
Probabilistic Boolean Networks (PBNs) have been previously proposed so as to gain insights into complex dy- namical systems. However, identification of large networks and of the underlying discrete Markov Chain which describes their temporal evolution, still remains a challenge. In this paper, we introduce an equivalent representation for the PBN, the Stochastic Conjunctive Normal Form (SCNF), which paves the way to a scalable learning algorithm and helps predict long- run dynamic behavior of large-scale systems. Moreover, SCNF allows its efficient sampling so as to statistically infer multi- …
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
Scaling probabilistic models to large realistic problems and datasets is a key challenge in machine learning. Central to this effort is the development of tractable probabilistic models (TPMs): models whose structure guarantees efficient probabilistic inference algorithms. The current landscape of TPMs is fragmented: there exist various kinds of TPMs with different strengths and weaknesses. Two of the most prominent classes of TPMs are determinantal point processes (DPPs) and probabilistic circuits (PCs). This paper provides the first systematic study of their relationship. We propose a unifie…
In recent years, several probabilistic techniques have been applied to various debugging problems. However, most existing probabilistic debugging systems use relatively simple statistical models, and fail to generalize across multiple programs. In this work, we propose Tractable Fault Localization Models (TFLMs) that can be learned from data, and probabilistically infer the location of the bug. While most previous statistical debugging methods generalize over many executions of a single program, TFLMs are trained on a corpus of previously seen buggy programs, and learn to identify recurring pa…
Probabilistic Circuits (PCs) are a promising avenue for probabilistic modeling. They combine advantages of probabilistic graphical models (PGMs) with those of neural networks (NNs). Crucially, however, they are tractable probabilistic models, supporting efficient and exact computation of many probabilistic inference queries, such as marginals and MAP. Further, since PCs are structured computation graphs, they can take advantage of deep-learning-style parameter updates, which greatly improves their scalability. However, this innovation also makes PCs prone to overfitting, which has been observe…
Probabilistic Circuits That Know What They Don't Know
TU Darmstadt（达姆施塔特工业大学）；Hessian Center for AI (hessian.AI)（黑森人工智能中心）；German Research Center for Artificial Intelligence (DFKI)（德国人工智能研究中心）；Centre for Cognitive Science TU Darmstadt（达姆施塔特工业大学认知科学中心）
Decision Trees are some of the most popular machine learning models today due to their out-of-the-box performance and interpretability. Often, Decision Trees models are constructed greedily in a top-down fashion via heuristic search criteria, such as Gini impurity or entropy. However, trees constructed in this manner are sensitive to minor fluctuations in training data and are prone to overfitting. In contrast, Bayesian approaches to tree construction formulate the selection process as a posterior inference problem; such approaches are more stable and provide greater theoretical guarantees. Ho…
Bayesian structure learning allows one to capture uncertainty over the causal directed acyclic graph (DAG) responsible for generating given data. In this work, we present Tractable Uncertainty for STructure learning (TRUST), a framework for approximate posterior inference that relies on probabilistic circuits as the representation of our posterior belief. In contrast to sample-based posterior approximations, our representation can capture a much richer space of DAGs, while also being able to tractably reason about the uncertainty through a range of useful inference queries. We empirically show…
Sum-Product Networks (SPNs) are expressive probabilistic models that provide exact, tractable inference. They achieve this efficiency by making use of local independence. On the other hand, mixtures of exchangeable variable models (MEVMs) are a class of tractable probabilistic models that make use of exchangeability of discrete random variables to render inference tractable. Exchangeability, which arises naturally in relational domains, has not been considered for efficient representation and inference in SPNs yet. The contribution of this paper is a novel probabilistic model which we call Exc…
University of Edinburgh（爱丁堡大学）；Alan Turing Institute（艾伦·图灵研究所）
Probabilistic representations, such as Bayesian and Markov networks, are fundamental to much of statistical machine learning. Thus, learning probabilistic representations directly from data is a deep challenge, the main computational bottleneck being inference that is intractable. Tractable learning is a powerful new paradigm that attempts to learn distributions that support efficient probabilistic querying. By leveraging local structure, representations such as sum-product networks (SPNs) can capture high tree-width models with many hidden layers, essentially a deep architecture, while still …
A sequence of random variables is exchangeable if its joint distribution is invariant under variable permutations. We introduce exchangeable variable models (EVMs) as a novel class of probabilistic models whose basic building blocks are partially exchangeable sequences, a generalization of exchangeable sequences. We prove that a family of tractable EVMs is optimal under zero-one loss for a large class of functions, including parity and threshold functions, and strictly subsumes existing tractable independence-based model families. Extensive experiments show that EVMs outperform state of the ar…
BiXSE: Improving Dense Retrieval via Probabilistic Graded Relevance Distillation
Université de Montéal（蒙特阿尔大学）；Mila - Quebec AI Institute（魁北克AI研究院）；McGill University（麦吉尔大学）；Apple MLR（苹果机器学习研究部）；IVADO, Canada（加拿大IVADO研究所）；CIFAR AI Chair（CIFAR人工智能主席）；ServiceNow Research（ServiceNow研究）
Hyperparameter Optimization via Interacting with Probabilistic Circuits
Computer Science Department, Technical University Darmstadt（技术大学达姆施塔特计算机科学系）；Hessian Center for AI (hessian.AI)（黑森人工智能中心）；German Research Center for AI (DFKI)（德国人工智能研究中心）
It is important to develop mathematically tractable models than can interpret knowledge extracted from the data and provide reasonable predictions. In this paper, we present a Linear Distillation Learning, a simple remedy to improve the performance of linear neural networks. Our approach is based on using a linear function for each class in a dataset, which is trained to simulate the output of a teacher linear network for each class separately. We tested our model on MNIST and Omniglot datasets in the Few-Shot learning manner. It showed better results than other interpretable models such as cl…
Einsum Networks: Fast and Scalable Learning of Tractable Probabilistic Circuits
Eindhoven University of Technology（埃因霍温理工大学）；Technical University Darmstadt（达姆施塔特技术大学）；Graz University of Technology（格拉茨理工大学）；University California Los Angeles（加州大学洛杉矶分校）；University of Cambridge（剑桥大学）
Probabilistic circuits (PCs) are a class of tractable probabilistic models that allow efficient, often linear-time, inference of queries such as marginals and most probable explanations (MPE). However, marginal MAP, which is central to many decision-making problems, remains a hard query for PCs unless they satisfy highly restrictive structural constraints. In this paper, we develop a pruning algorithm that removes parts of the PC that are irrelevant to a marginal MAP query, shrinking the PC while maintaining the correct solution. This pruning technique is so effective that we are able to build…
Computer Science Department, University of California, Los Angeles（加州大学洛杉矶分校计算机科学系）
Tractable Boolean and arithmetic circuits have been studied extensively in AI for over two decades now. These circuits were initially proposed as "compiled objects," meant to facilitate logical and probabilistic reasoning, as they permit various types of inference to be performed in linear-time and a feed-forward fashion like neural networks. In more recent years, the role of tractable circuits has significantly expanded as they became a computational and semantical backbone for some approaches that aim to integrate knowledge, reasoning and learning. In this article, we review the foundations …
University of Edinburgh（爱丁堡大学）；Alan Turing Institute（艾伦·图灵研究所）
Probabilistic representations, such as Bayesian and Markov networks, are fundamental to much of statistical machine learning. Thus, learning probabilistic representations directly from data is a deep challenge, the main computational bottleneck being inference that is intractable. Tractable learning is a powerful new paradigm that attempts to learn distributions that support efficient probabilistic querying. By leveraging local structure, representations such as sum-product networks (SPNs) can capture high tree-width models with many hidden layers, essentially a deep architecture, while still …
