论文检索

Applications/Genetics, Cell Biology, etc

Tianyu Xie, Cheng Zhang

Designing flexible probabilistic models over tree topologies is important for developing efficient phylogenetic inference methods. To do that, previous works often leverage the similarity of tree topologies via hand-engineered heuristic features which would require domain expertise and may suffer from limited approximation capability. In this paper, we propose a deep autoregressive model for phylogenetic inference based on graph neural networks (GNNs), called ARTree. By decomposing a tree topology into a sequence of leaf node addition operations and modeling the involved conditional distributions based on learnable topological features via GNNs, ARTree can provide a rich family of distributions over tree topologies that have simple sampling algorithms, without using heuristic features. We demonstrate the effectiveness and efficiency of our method on a benchmark of challenging real data tree topology density estimation and variational Bayesian phylogenetic inference problems.

Probabilistic Methods/Variational Inference

Saurav Jha, Dong Gong, He Zhao, Lina Yao

Continual learning (CL) aims to train deep neural networks efficiently on streaming data while limiting the forgetting caused by new tasks. However, learning transferable knowledge with less interference between tasks is difficult, and real-world deployment of CL models is limited by their inability to measure predictive uncertainties. To address these issues, we propose handling CL tasks with neural processes (NPs), a class of meta-learners that encode different tasks into probabilistic distributions over functions all while providing reliable uncertainty estimates. Specifically, we propose an NP-based CL approach (NPCL) with task-specific modules arranged in a hierarchical latent variable model. We tailor regularizers on the learned latent distributions to alleviate forgetting. The uncertainty estimation capabilities of the NPCL can also be used to handle the task head/module inference challenge in CL. Our experiments show that the NPCL outperforms previous CL approaches. We validate the effectiveness of uncertainty estimation in the NPCL for identifying novel data and evaluating instance-level model confidence. Code is available at https://github.com/srvCodes/NPCL.

Probabilistic Methods/Bayesian Models and Methods

Van-Anh Nguyen, Tung-Long Vuong, Hoang Phan, Thanh-Toan Do, Dinh Phung, Trung Le

Bayesian Neural Networks (BNNs) provide a probabilistic interpretation for deep learning models by imposing a prior distribution over model parameters and inferring a posterior distribution based on observed data. The model sampled from the posterior distribution can be used for providing ensemble predictions and quantifying prediction uncertainty. It is well-known that deep learning models with lower sharpness have better generalization ability. However, existing posterior inferences are not aware of sharpness/flatness in terms of formulation, possibly leading to high sharpness for the models sampled from them. In this paper, we develop theories, the Bayesian setting, and the variational inference approach for the sharpness-aware posterior. Specifically, the models sampled from our sharpness-aware posterior, and the optimal approximate posterior estimating this sharpness-aware posterior, have better flatness, hence possibly possessing higher generalization ability. We conduct experiments by leveraging the sharpness-aware posterior with state-of-the-art Bayesian Neural Networks, showing that the flat-seeking counterparts outperform their baselines in all metrics of interest.

Probabilistic Methods/Variational Inference

Ziheng Cheng, Shiyue Zhang, Longlin Yu, Cheng Zhang

Particle-based variational inference methods (ParVIs) such as Stein variational gradient descent (SVGD) update the particles based on the kernelized Wasserstein gradient flow for the Kullback-Leibler (KL) divergence. However, the design of kernels is often non-trivial and can be restrictive for the flexibility of the method. Recent works show that functional gradient flow approximations with quadratic form regularization terms can improve performance. In this paper, we propose a ParVI framework, called generalized Wasserstein gradient descent (GWG), based on a generalized Wasserstein gradient flow of the KL divergence, which can be viewed as a functional gradient method with a broader class of regularizers induced by convex functions. We show that GWG exhibits strong convergence guarantees. We also provide an adaptive version that automatically chooses Wasserstein metric to accelerate convergence. In experiments, we demonstrate the effectiveness and efficiency of the proposed framework on both simulated and real data problems.

Probabilistic Methods/Graphical Models

Shivani Bathla, Vinita Vasudevan

Exact inference of marginals in probabilistic graphical models (PGM) is known to be intractable, necessitating the use of approximate methods. Most of the existing variational techniques perform iterative message passing in loopy graphs which is slow to converge for many benchmarks. In this paper, we propose a new algorithm for marginal inference that is based on the incremental build-infer-approximate (IBIA) paradigm. Our algorithm converts the PGM into a sequence of linked clique tree forests (SLCTF) with bounded clique sizes, and then uses a heuristic belief update algorithm to infer the marginals. For the special case of Bayesian networks, we show that if the incremental build step in IBIA uses the topological order of variables then (a) the prior marginals are consistent in all CTFs in the SLCTF and (b) the posterior marginals are consistent once all evidence variables are added to the SLCTF. In our approach, the belief propagation step is non-iterative and the accuracy-complexity trade-off is controlled using user-defined clique size bounds. Results for several benchmark sets from recent UAI competitions show that our method gives either better or comparable accuracy than existing variational and sampling based methods, with smaller runtimes.

Applications/Physics

Fabien Casenave, Brian Staber, Xavier Roynard

When learning simulations for modeling physical phenomena in industrial designs, geometrical variabilities are of prime interest. While classical regression techniques prove effective for parameterized geometries, practical scenarios often involve the absence of shape parametrization during the inference stage, leaving us with only mesh discretizations as available data. Learning simulations from such mesh-based representations poses significant challenges, with recent advances relying heavily on deep graph neural networks to overcome the limitations of conventional machine learning approaches. Despite their promising results, graph neural networks exhibit certain drawbacks, including their dependency on extensive datasets and limitations in providing built-in predictive uncertainties or handling large meshes. In this work, we propose a machine learning method that do not rely on graph neural networks. Complex geometrical shapes and variations with fixed topology are dealt with using well-known mesh morphing onto a common support, combined with classical dimensionality reduction techniques and Gaussian processes. The proposed methodology can easily deal with large meshes without the need for explicit shape parameterization and provides crucial predictive uncertainties, which are essential for informed decision-making. In the considered numerical experiments, the proposed method is competitive with respect to existing graph neural networks, regarding training efficiency and accuracy of the predictions.

Reinforcement Learning

Yihang Yao, ZUXIN LIU, Zhepeng Cen, Jiacheng Zhu, Wenhao Yu, Tingnan Zhang, DING ZHAO

Safe reinforcement learning (RL) focuses on training reward-maximizing agents subject to pre-defined safety constraints. Yet, learning versatile safe policies that can adapt to varying safety constraint requirements during deployment without retraining remains a largely unexplored and challenging area. In this work, we formulate the versatile safe RL problem and consider two primary requirements: training efficiency and zero-shot adaptation capability. To address them, we introduce the Conditioned Constrained Policy Optimization (CCPO) framework, consisting of two key modules: (1) Versatile Value Estimation (VVE) for approximating value functions under unseen threshold conditions, and (2) Conditioned Variational Inference (CVI) for encoding arbitrary constraint thresholds during policy optimization. Our extensive experiments demonstrate that CCPO outperforms the baselines in terms of safety and task performance while preserving zero-shot adaptation capabilities to different constraint thresholds data-efficiently. This makes our approach suitable for real-world dynamic applications.

Probabilistic Methods/Monte Carlo and Sampling Methods

Oren Mangoubi, Nisheeth K. Vishnoi

Given a Lipschitz or smooth convex function $f:K \to \mathbb{R}^d$ for a bounded polytope $K:=${ $\theta \in \mathbb{R}^d: A\theta \leq b$}, where $A\in \mathbb{R}^{m\times d}$ and $b \in \mathbb{R}^m$, we consider the problem of sampling from the log-concave distribution $\pi(\theta) \propto e^{-f(\theta)}$ constrained to $K$. Interest in this problem derives from its applications to Bayesian inference and differential privacy. We present a generalization of the Dikin walk to this setting that requires at most $O((md + d L^2 R^2) \times md^{\omega-1} \log(\frac{w}{\delta}))$ arithmetic operations to sample from $\pi$ within error $\delta>0$ in the total variation distance from a $w$-warm start. Here $L$ is the Lipschitz constant of $f$, $K$ is contained in a ball of radius $R$ and contains a ball of smaller radius $r$, and $\omega \approx 2.37$ is the matrix-multiplication constant. This improves on the running time of prior works for a range of structured settings important for the aforementioned inference and privacy applications. Technically, we depart from previous Dikin walks by adding a soft-threshold regularizer derived from the Lipschitz or smoothness properties of $f$ to a barrier function for $K$ that allows our version of the Dikin walk to propose updates that have a high Metropolis acceptance ratio for $f$, while at the same time remaining inside the polytope $K$.

Miscellaneous Aspects of Machine Learning/Causality

Valentyn Melnychuk, Dennis Frauen, Stefan Feuerriegel

Counterfactual inference aims to answer retrospective "what if" questions and thus belongs to the most fine-grained type of inference in Pearl's causality ladder. Existing methods for counterfactual inference with continuous outcomes aim at point identification and thus make strong and unnatural assumptions about the underlying structural causal model. In this paper, we relax these assumptions and aim at partial counterfactual identification of continuous outcomes, i.e., when the counterfactual query resides in an ignorance interval with informative bounds. We prove that, in general, the ignorance interval of the counterfactual queries has non-informative bounds, already when functions of structural causal models are continuously differentiable. As a remedy, we propose a novel sensitivity model called Curvature Sensitivity Model. This allows us to obtain informative bounds by bounding the curvature of level sets of the functions. We further show that existing point counterfactual identification methods are special cases of our Curvature Sensitivity Model when the bound of the curvature is set to zero. We then propose an implementation of our Curvature Sensitivity Model in the form of a novel deep generative model, which we call Augmented Pseudo-Invertible Decoder. Our implementation employs (i) residual normalizing flows with (ii) variational augmentations. We empirically demonstrate the effectiveness of our Augmented Pseudo-Invertible Decoder. To the best of our knowledge, ours is the first partial identification model for Markovian structural causal models with continuous outcomes.

Miscellaneous Aspects of Machine Learning/Unsupervised and Semi-supervised Learning

Thomas Sutter, Alain Ryser, Joram Liebeskind, Julia Vogt

Partitioning a set of elements into an unknown number of mutually exclusive subsets is essential in many machine learning problems.However, assigning elements, such as samples in a dataset or neurons in a network layer, to an unknown and discrete number of subsets is inherently non-differentiable, prohibiting end-to-end gradient-based optimization of parameters.We overcome this limitation by proposing a novel two-step method for inferring partitions, which allows its usage in variational inference tasks.This new approach enables reparameterized gradients with respect to the parameters of the new random partition model.Our method works by inferring the number of elements per subset and, second, by filling these subsets in a learned order.We highlight the versatility of our general-purpose approach on three different challenging experiments: variational clustering, inference of shared and independent generative factors under weak supervision, and multitask learning.

Reinforcement Learning

Jean Tarbouriech, Tor Lattimore, Brendan O'Donoghue

A popular perspective in Reinforcement learning (RL) casts the problem as probabilistic inference on a graphical model of the Markov decision process (MDP). The core object of study is the probability of each state-action pair being visited under the optimal policy. Previous approaches to approximate this quantity can be arbitrarily poor, leading to algorithms that do not implement genuine statistical inference and consequently do not perform well in challenging problems. In this work, we undertake a rigorous Bayesian treatment of the posterior probability of state-action optimality and clarify how it flows through the MDP. We first reveal that this quantity can indeed be used to generate a policy that explores efficiently, as measured by regret. Unfortunately, computing it is intractable, so we derive a new variational Bayesian approximation yielding a tractable convex optimization problem and establish that the resulting policy also explores efficiently. We call our approach VAPOR and show that it has strong connections to Thompson sampling, K-learning, and maximum entropy exploration. We conclude with some experiments demonstrating the performance advantage of a deep RL version of VAPOR.

Theory

Dor Tsur, Ziv Goldfeld, Kristjan Greenewald

Quantifying dependence between high-dimensional random variables is central to statistical learning and inference. Two classical methods are canonical correlation analysis (CCA), which identifies maximally correlated projected versions of the original variables, and Shannon's mutual information, which is a universal dependence measure that also captures high-order dependencies. However, CCA only accounts for linear dependence, which may be insufficient for certain applications, while mutual information is often infeasible to compute/estimate in high dimensions. This work proposes a middle ground in the form of a scalable information-theoretic generalization of CCA, termed max-sliced mutual information (mSMI). mSMI equals the maximal mutual information between low-dimensional projections of the high-dimensional variables, which reduces back to CCA in the Gaussian case. It enjoys the best of both worlds: capturing intricate dependencies in the data while being amenable to fast computation and scalable estimation from samples. We show that mSMI retains favorable structural properties of Shannon's mutual information, like variational forms and identification of independence. We then study statistical estimation of mSMI, propose an efficiently computable neural estimator, and couple it with formal non-asymptotic error bounds. We present experiments that demonstrate the utility of mSMI for several tasks, encompassing independence testing, multi-view representation learning, algorithmic fairness, and generative modeling. We observe that mSMI consistently outperforms competing methods with little-to-no computational overhead.

Probabilistic Methods/Bayesian Models and Methods

Caleb Dahlke, Jason Pacheco

Gaussian mixture models (GMMs) are fundamental to machine learning due to their flexibility as approximating densities. However, uncertainty quantification of GMMs remains a challenge as differential entropy lacks a closed form. This paper explores polynomial approximations, specifically Taylor and Legendre, to the GMM entropy from a theoretical and practical perspective. We provide new analysis of a widely used approach due to Huber et al.(2008) and show that the series diverges under simple conditions. Motivated by this divergence we provide a novel Taylor series that is provably convergent to the true entropy of any GMM. We demonstrate a method for selecting a center such that the series converges from below, providing a lower bound on GMM entropy. Furthermore, we demonstrate that orthogonal polynomial series result in more accurate polynomial approximations. Experimental validation supports our theoretical results while showing that our method is comparable in computation to Huber et al. We also show that in application, the use of these polynomial approximations, such as in Nonparametric Variational Inference by Gershamn et al. (2012), rely on the convergence of the methods in computing accurate approximations. This work contributes useful analysis to existing methods while introducing a novel approximation supported by firm theoretical guarantees.

Probabilistic Methods/Bayesian Models and Methods

Balhae Kim, Hyungi Lee, Juho Lee

A Bayesian pseudocoreset is a compact synthetic dataset summarizing essential information of a large-scale dataset and thus can be used as a proxy dataset for scalable Bayesian inference. Typically, a Bayesian pseudocoreset is constructed by minimizing a divergence measure between the posterior conditioning on the pseudocoreset and the posterior conditioning on the full dataset. However, evaluating the divergence can be challenging, particularly for the models like deep neural networks having high-dimensional parameters. In this paper, we propose a novel Bayesian pseudocoreset construction method that operates on a function space. Unlike previous methods, which construct and match the coreset and full data posteriors in the space of model parameters (weights), our method constructs variational approximations to the coreset posterior on a function space and matches it to the full data posterior in the function space. By working directly on the function space, our method could bypass several challenges that may arise when working on a weight space, including limited scalability and multi-modality issue. Through various experiments, we demonstrate that the Bayesian pseudocoresets constructed from our method enjoys enhanced uncertainty quantification and better robustness across various model architectures.

Reinforcement Learning/Batch Offline

Jiayi Guan, Guang Chen, Jiaming Ji, Long Yang, ao zhou, Zhijun Li, changjun jiang

Offline safe reinforcement learning (RL) algorithms promise to learn policies that satisfy safety constraints directly in offline datasets without interacting with the environment. This arrangement is particularly important in scenarios with high sampling costs and potential dangers, such as autonomous driving and robotics. However, the influence of safety constraints and out-of-distribution (OOD) actions have made it challenging for previous methods to achieve high reward returns while ensuring safety. In this work, we propose a Variational Optimization with Conservative Eestimation algorithm (VOCE) to solve the problem of optimizing safety policies in the offline dataset. Concretely, we reframe the problem of offline safe RL using probabilistic inference, which introduces variational distributions to make the optimization of policies more flexible. Subsequently, we utilize pessimistic estimation methods to estimate the Q-value of cost and reward, which mitigates the extrapolation errors induced by OOD actions. Finally, extensive experiments demonstrate that the VOCE algorithm achieves competitive performance across multiple experimental tasks, particularly outperforming state-of-the-art algorithms in terms of safety.

Applications/Physics

Michael Scherbela, Leon Gerard, Philipp Grohs

Obtaining accurate solutions to the Schrödinger equation is the key challenge in computational quantum chemistry. Deep-learning-based Variational Monte Carlo (DL-VMC) has recently outperformed conventional approaches in terms of accuracy, but only at large computational cost.Whereas in many domains models are trained once and subsequently applied for inference, accurate DL-VMC so far requires a full optimization for every new problem instance, consuming thousands of GPUhs even for small molecules.We instead propose a DL-VMC model which has been pre-trained using self-supervised wavefunction optimization on a large and chemically diverse set of molecules. Applying this model to new molecules without any optimization, yields wavefunctions and absolute energies that outperform established methods such as CCSD(T)-2Z.To obtain accurate relative energies, only few fine-tuning steps of this base model are required.We accomplish this with a fully end-to-end machine-learned model, consisting of an improved geometry embedding architecture and an existing SE(3)-equivariant model to represent molecular orbitals. Combining this architecture with continuous sampling of geometries, we improve zero-shot accuracy by two orders of magnitude compared to the state of the art.We extensively evaluate the accuracy, scalability and limitations of our base model on a wide variety of test systems.

Probabilistic Methods/Monte Carlo and Sampling Methods

Yuling Yao, Justin Domke

To check the accuracy of Bayesian computations, it is common to use rank-based simulation-based calibration (SBC). However, SBC has drawbacks: The test statistic is somewhat ad-hoc, interactions are difficult to examine, multiple testing is a challenge, and the resulting p-value is not a divergence metric. We propose to replace the marginal rank test with a flexible classification approach that learns test statistics from data. This measure typically has a higher statistical power than the SBC test and returns an interpretable divergence measure of miscalibration, computed from classification accuracy. This approach can be used with different data generating processes to address simulation-based inference or traditional inference methods like Markov chain Monte Carlo or variational inference. We illustrate an automated implementation using neural networks and statistically-inspired features, and validate the method with numerical and real data experiments.

Applications/Neuroscience, Cognitive Science

Hadi Vafaii, Jacob Yates, Daniel Butts

The relationship between perception and inference, as postulated by Helmholtz in the 19th century, is paralleled in modern machine learning by generative models like Variational Autoencoders (VAEs) and their hierarchical variants. Here, we evaluate the role of hierarchical inference and its alignment with brain function in the domain of motion perception. We first introduce a novel synthetic data framework, Retinal Optic Flow Learning (ROFL), which enables control over motion statistics and their causes. We then present a new hierarchical VAE and test it against alternative models on two downstream tasks: (i) predicting ground truth causes of retinal optic flow (e.g., self-motion); and (ii) predicting the responses of neurons in the motion processing pathway of primates. We manipulate the model architectures (hierarchical versus non-hierarchical), loss functions, and the causal structure of the motion stimuli. We find that hierarchical latent structure in the model leads to several improvements. First, it improves the linear decodability of ground truth variables and does so in a sparse and disentangled manner. Second, our hierarchical VAE outperforms previous state-of-the-art models in predicting neuronal responses and exhibits sparse latent-to-neuron relationships. These results depend on the causal structure of the world, indicating that alignment between brains and artificial neural networks depends not only on architecture but also on matching ecologically relevant stimulus statistics. Taken together, our results suggest that hierarchical Bayesian inference underlines the brain's understanding of the world, and hierarchical VAEs can effectively model this understanding.

Probabilistic Methods/Graphical Models

Marcello Massimo Negri, Fabricio Arend Torres, Volker Roth

Studying conditional independence among many variables with few observations is a challenging task.Gaussian Graphical Models (GGMs) tackle this problem by encouraging sparsity in the precision matrix through $l_q$ regularization with $q\leq1$.However, most GMMs rely on the $l_1$ norm because the objective is highly non-convex for sub-$l_1$ pseudo-norms.In the frequentist formulation, the $l_1$ norm relaxation provides the solution path as a function of the shrinkage parameter $\lambda$.In the Bayesian formulation, sparsity is instead encouraged through a Laplace prior, but posterior inference for different $\lambda$ requires repeated runs of expensive Gibbs samplers.Here we propose a general framework for variational inference with matrix-variate Normalizing Flow in GGMs, which unifies the benefits of frequentist and Bayesian frameworks.As a key improvement on previous work, we train with one flow a continuum of sparse regression models jointly for all regularization parameters $\lambda$ and all $l_q$ norms, including non-convex sub-$l_1$ pseudo-norms.Within one model we thus have access to (i) the evolution of the posterior for any $\lambda$ and any $l_q$ (pseudo-) norm, (ii) the marginal log-likelihood for model selection, and (iii) the frequentist solution paths through simulated annealing in the MAP limit.

Deep Learning/Graph Neural Networks

Senzhang Wang, Jun Yin, Chaozhuo Li, Xing Xie, Jianxin Wang

GNN explanation method aims to identify an explanatory subgraph which contains the most informative components of the full graph. However, a major limitation of existing GNN explainers is that they are not robust to the structurally corrupted graphs, e.g., graphs with noisy or adversarial edges. On the one hand, existing GNN explainers mostly explore explanations based on either the raw graph features or the learned latent representations, both of which can be easily corrupted. On the other hand, the corruptions in graphs are irregular in terms of the structural properties, e.g., the size or connectivity of graphs, which makes the rigorous constraints used by previous GNN explainers unfeasible. To address these issues, we propose a robust GNN explainer called V-InfoR. Specifically, a robust graph representation extractor, which takes insights of variational inference, is proposed to infer the latent distribution of graph representations. Instead of directly using the corrupted raw features or representations of each single graph, we sample the graph representations from the inferred distribution for the downstream explanation generator, which can effectively eliminate the minor corruption. We next formulate the explanation exploration as a graph information bottleneck (GIB) optimization problem. As a more general method that does not need any rigorous structural constraints, our GIB-based method can adaptively capture both the regularity and irregularity of the severely corrupted graphs for explanation. Extensive evaluations on both synthetic and real-world datasets indicate that V-InfoR significantly improves the GNN explanation performance for the structurally corrupted graphs. Code and dataset are available at https://anonymous.4open.science/r/V-InfoR-EF88