论文检索

Probabilistic Methods · Variational Inference

Alessandro Mastrototaro, Jimmy Olsson

Being the most classical generative model for serial data, state-space models (SSM) are fundamental in AI and statistical machine learning. In SSM, any form of parameter learning or latent state inference typically involves the computation of complex latent-state posteriors. In this work, we build upon the variational sequential Monte Carlo (VSMC) method, which provides computationally efficient and accurate model parameter estimation and Bayesian latent-state inference by combining particle methods and variational inference. While standard VSMC operates in the offline mode, by re-processing repeatedly a given batch of data, we distribute the approximation of the gradient of the VSMC surrogate ELBO in time using stochastic approximation, allowing for online learning in the presence of streams of data. This results in an algorithm, online VSMC, that is capable of performing efficiently, entirely on-the-fly, both parameter estimation and particle proposal adaptation. In addition, we provide rigorous theoretical results describing the algorithm's convergence properties as the number of data tends to infinity as well as numerical illustrations of its excellent convergence properties and usefulness also in batch-processing settings.

Deep Learning · Graph Neural Networks

Jaejun Lee, Minsung Hwang, Joyce Whang

While a number of knowledge graph representation learning (KGRL) methods have been proposed over the past decade, very few theoretical analyses have been conducted on them. In this paper, we present the first PAC-Bayesian generalization bounds for KGRL methods. To analyze a broad class of KGRL models, we propose a generic framework named ReED (Relation-aware Encoder-Decoder), which consists of a relation-aware message passing encoder and a triplet classification decoder. Our ReED framework can express at least 15 different existing KGRL models, including not only graph neural network-based models such as R-GCN and CompGCN but also shallow-architecture models such as RotatE and ANALOGY. Our generalization bounds for the ReED framework provide theoretical grounds for the commonly used tricks in KGRL, e.g., parameter-sharing and weight normalization schemes, and guide desirable design choices for practical KGRL methods. We empirically show that the critical factors in our generalization bounds can explain actual generalization errors on three real-world knowledge graphs.

Probabilistic Methods · Bayesian Models and Methods

Sergio Calvo Ordoñez, Matthieu Meunier, Francesco Piatti, Yuantao Shi

In this paper, we present Partially Stochastic Infinitely Deep Bayesian Neural Networks, a novel family of architectures that integrates partial stochasticity into the framework of infinitely deep neural networks. Our new class of architectures is designed to improve the computational efficiency of existing architectures at training and inference time. To do this, we leverage the advantages of partial stochasticity in the infinite-depth limit which include the benefits of full stochasticity e.g. robustness, uncertainty quantification, and memory efficiency, whilst improving their limitations around computational complexity. We present a variety of architectural configurations, offering flexibility in network design including different methods for weight partition. We also provide mathematical guarantees on the expressivity of our models by establishing that our network family qualifies as Universal Conditional Distribution Approximators. Lastly, empirical evaluations across multiple tasks show that our proposed architectures achieve better downstream task performance and uncertainty quantification than their counterparts while being significantly more efficient. The code can be found at https://github.com/Sergio20f/part_stoch_inf_deep

Probabilistic Methods · Bayesian Models and Methods

Yirui Liu, Xinghao Qiao, Yulong Pei, Liying Wang

This paper introduces the Deep Functional Factor Model (DF2M), a Bayesian nonparametric model designed for analysis of high-dimensional functional time series. DF2M is built upon the Indian Buffet Process and the multi-task Gaussian Process, incorporating a deep kernel function that captures non-Markovian and nonlinear temporal dynamics. Unlike many black-box deep learning models, DF2M offers an explainable approach to utilizing neural networks by constructing a factor model and integrating deep neural networks within the kernel function. Additionally, we develop a computationally efficient variational inference algorithm to infer DF2M. Empirical results from four real-world datasets demonstrate that DF2M provides better explainability and superior predictive accuracy compared to conventional deep learning models for high-dimensional functional time series.

Yibo Zhou, Hai-Miao Hu, Yirong Xiang, Xiaokang Zhang, Haotian Wu

Rooting in the scarcity of most attributes, realistic pedestrian attribute datasets exhibit unduly skewed data distribution, from which two types of model failures are delivered: (1) label imbalance: model predictions lean greatly towards the side of majority labels; (2) semantics imbalance: model is easily overfitted on the under-represented attributes due to their insufficient semantic diversity. To render perfect label balancing, we propose a novel framework that successfully decouples label-balanced data re-sampling from the curse of attributes co-occurrence, i.e., we equalize the sampling prior of an attribute while not biasing that of the co-occurred others. To diversify the attributes semantics and mitigate the feature noise, we propose a Bayesian feature augmentation method to introduce true in-distribution novelty. Handling both imbalances jointly, our work achieves best accuracy on various popular benchmarks, and importantly, with minimal computational budget.

Social Aspects · Trustworthy Machine Learning

Zhenyi Wang, Yihan Wu, Heng Huang

Model extraction is to obtain a cloned model that replicates the functionality of a black-box victim model solely through query-based access. Present defense strategies exhibit shortcomings, manifesting as: (1) computational or memory inefficiencies during deployment; or (2) dependence on expensive defensive training methods that mandate the re-training of the victim model; or (3) watermarking-based methods only *passively* detect model theft without actively preventing model extraction. To address these limitations, we introduce an innovative Bayesian *active* watermarking technique to fine-tune the victim model and learn the watermark posterior distribution conditioned on input data. The fine-tuning process aims to maximize the log-likelihood on watermarked in-distribution training data for preserving model utility while simultaneously maximizing the change of model's outputs on watermarked out-of-distribution data, thereby achieving effective defense. During deployment, a watermark is randomly sampled from the estimated watermark posterior. This watermark is then added to the input query, and the victim model returns the prediction based on the watermarked input query to users. This proactive defense approach requires only slight fine-tuning of the victim model without the need of full re-training and demonstrates high efficiency in terms of memory and computation during deployment. Rigorous theoretical analysis and comprehensive experimental results demonstrate the efficacy of our proposed method.

Probabilistic Methods · Bayesian Models and Methods

Yasen Wang, Junlin Li, Zuogong Yue, Ye Yuan

As a well-known machine learning algorithm, sparse Bayesian learning (SBL) can find sparse representations in linearly probabilistic models by imposing a sparsity-promoting prior on model coefficients. However, classical SBL algorithms lack the essential theoretical guarantees of global convergence. To address this issue, we propose an iterative Min-Min optimization method to solve the marginal likelihood function (MLF) of SBL based on the concave-convex procedure. The method can optimize the hyperparameters related to both the prior and noise level analytically at each iteration by re-expressing MLF using auxiliary functions. Particularly, we demonstrate that the method globally converges to a local minimum or saddle point of MLF. With rigorous theoretical guarantees, the proposed novel SBL algorithm outperforms classical ones in finding sparse representations on simulation and real-world examples, ranging from sparse signal recovery to system identification and kernel regression.

Deep Learning · Graph Neural Networks

See Hian Lee, Feng Ji, Kelin Xia, Wee Peng Tay

Traditionally, graph neural networks have been trained using a single observed graph. However, the observed graph represents only one possible realization. In many applications, the graph may encounter uncertainties, such as having erroneous or missing edges, as well as edge weights that provide little informative value. To address these challenges and capture additional information previously absent in the observed graph, we introduce latent variables to parameterize and generate multiple graphs. The parameters follow an unknown distribution to be estimated. We propose a formulation in terms of maximum likelihood estimation of the network parameters. Therefore, it is possible to devise an algorithm based on Expectation-Maximization (EM). Specifically, we iteratively determine the distribution of the graphs using a Markov Chain Monte Carlo (MCMC) method, incorporating the principles of PAC-Bayesian theory. Numerical experiments demonstrate improvements in performance against baseline models on node classification for both heterogeneous and homogeneous graphs.

Deep Learning · Large Language Models

Weixi Song, Zuchao Li, Lefei Zhang, hai zhao, Bo Du

With the prevalence of pre-training-fine-tuning paradigm, how to efficiently adapt the pre-trained model to the downstream tasks has been an intriguing issue. $\textbf{P}$arameter-$\textbf{E}$fficient $\textbf{F}$ine-$\textbf{T}$uning(PEFT) methods have been proposed for low-cost adaptation. Although PEFT has demonstrated effectiveness and been widely applied, the underlying principles are still unclear. In this paper, we adopt the PAC-Bayesian generalization error bound, viewing pre-training as a shift of prior distribution which leads to a tighter bound for generalization error. We validate this shift from the perspectives of oscillations in the loss landscape and the quasi-sparsity in gradient distribution. Based on this, we propose a gradient-based sparse fine-tuning algorithm, named $\textbf{S}$parse $\textbf{I}$ncrement $\textbf{F}$ine-$\textbf{T}$uning(SIFT), and validate its effectiveness on a range of tasks including the GLUE Benchmark and Instruction-tuning. The code is accessible at https://github.com/song-wx/SIFT/.

Probabilistic Methods · Bayesian Models and Methods

Emanuel Sommer, Lisa Wimmer, Theodore Papamarkou, Ludwig Bothmann, Bernd Bischl, David Rügamer

A major challenge in sample-based inference (SBI) for Bayesian neural networks is the size and structure of the networks’ parameter space. Our work shows that successful SBI is possible by embracing the characteristic relationship between weight and function space, uncovering a systematic link between overparameterization and the difficulty of the sampling problem. Through extensive experiments, we establish practical guidelines for sampling and convergence diagnosis. As a result, we present a deep ensemble initialized approach as an effective solution with competitive performance and uncertainty quantification.

Probabilistic Methods · Bayesian Models and Methods

Paulo Soares, Adarsh Pyarelal, Meghavarshini Krishnaswamy, Emily Butler, Kobus Barnard

We develop a novel probabilistic model for interpersonal coordination as a latent phenomenon explaining statistical temporal influence between multiple components in a system. For example, the state of one person can influence that of another at a later time, as indicated by their observed behaviors. We characterize coordination as the degree to which the distributions for such states at one time point are merged for the next salient time point. We evaluate our model in the context of three-person teams executing a virtual search and rescue (SAR) mission. We first use synthetic data to confirm that our technical definition of coordination is consistent with expectations and that we can recover generated coordination despite noise. We then show that captured coordination can be predictive of team performance on real data. Here we use speech vocalics and semantics to infer coordination for 36 teams carrying out two successive SAR missions. In two different datasets, we find that coordination is generally predictive of team score for the second mission, but not for the first, where teams are largely learning to play the game. In addition, we found that including a semantic modality improves prediction in some scenarios. This shows that our intuitive technical definition can capture useful explanatory aspects of team behavior.

Deep Learning · Generative Models and Autoencoders

Tiago Silva, Luiz Carvalho, Amauri Souza, Samuel Kaski, Diego Mesquita

GFlowNets are a promising alternative to MCMC sampling for discrete compositional random variables. Training GFlowNets requires repeated evaluations of the unnormalized target distribution, or reward function. However, for large-scale posterior sampling, this may be prohibitive since it incurs traversing the data several times. Moreover, if the data are distributed across clients, employing standard GFlowNets leads to intensive client-server communication. To alleviate both these issues, we propose _embarrassingly parallel_ GFlowNet (EP-GFlowNet). EP-GFlowNet is a provably correct divide-and-conquer method to sample from product distributions of the form $R(\cdot) \propto R_1(\cdot) ... R_N(\cdot)$ --- e.g., in parallel or federated Bayes, where each $R_n$ is a local posterior defined on a data partition. First, in parallel, we train a local GFlowNet targeting each $R_n$ and send the resulting models to the server. Then, the server learns a global GFlowNet by enforcing our newly proposed _aggregating balance_ condition, requiring a single communication step. Importantly, EP-GFlowNets can also be applied to multi-objective optimization and model reuse. Our experiments illustrate the effectiveness of EP-GFlowNets on multiple tasks, including parallel Bayesian phylogenetics, multi-objective multiset and sequence generation, and federated Bayesian structure learning.

Miscellaneous Aspects of Machine Learning · Online Learning, Active Learning and Bandits

Jeevan Thapa, Rui Li

While existing dynamic architecture-based continual learning methods adapt network width by growing new branches, they overlook the critical aspect of network depth. We propose a novel non-parametric Bayesian approach to infer network depth and adapt network width while maintaining model performance across tasks. Specifically, we model the growth of network depth with a beta process and apply drop-connect regularization to network width using a conjugate Bernoulli process. Our results show that our proposed method achieves superior or comparable performance with state-of-the-art methods across various continual learning benchmarks. Moreover, our approach can be readily extended to unsupervised continual learning, showcasing competitive performance compared to existing techniques.

Probabilistic Methods · Bayesian Models and Methods

Cornelius Schröder, Jakob Macke

Many scientific models are composed of multiple discrete components, and scientists often make heuristic decisions about which components to include. Bayesian inference provides a mathematical framework for systematically selecting model components, but defining prior distributions over model components and developing associated inference schemes has been challenging. We approach this problem in a simulation-based inference framework: We define model priors over candidate components and, from model simulations, train neural networks to infer joint probability distributions over both model components and associated parameters. Our method, simulation-based model inference (SBMI), represents distributions over model components as a conditional mixture of multivariate binary distributions in the Grassmann formalism. SBMI can be applied to any compositional stochastic simulator without requiring likelihood evaluations. We evaluate SBMI on a simple time series model and on two scientific models from neuroscience, and show that it can discover multiple data-consistent model configurations, and that it reveals non-identifiable model components and parameters. SBMI provides a powerful tool for data-driven scientific inquiry which will allow scientists to identify essential model components and make uncertainty-informed modelling decisions.

Probabilistic Methods · Bayesian Models and Methods

Marvin Schmitt, Desi Ivanova, Daniel Habermann, Ullrich Koethe, Paul Buerkner, Stefan Radev

We propose a method to improve the efficiency and accuracy of amortized Bayesian inference by leveraging universal symmetries in the joint probabilistic model of parameters and data. In a nutshell, we invert Bayes' theorem and estimate the marginal likelihood based on approximate representations of the joint model. Upon perfect approximation, the marginal likelihood is constant across all parameter values by definition. However, errors in approximate inference lead to undesirable variance in the marginal likelihood estimates across different parameter values. We penalize violations of this symmetry with a self-consistency loss which significantly improves the quality of approximate inference in low data regimes and can be used to augment the training of popular neural density estimators. We apply our method to a number of synthetic problems and realistic scientific models, discovering notable advantages in the context of both neural posterior and likelihood approximation.

Theory · Online Learning and Bandits

Sudeep Salgia, Sattar Vakili, Qing Zhao

We consider Bayesian optimization using Gaussian Process models, also referred to as kernel-based bandit optimization. We study the methodology of exploring the domain using random samples drawn from a distribution. We show that this random exploration approach achieves the optimal error rates. Our analysis is based on novel concentration bounds in an infinite dimensional Hilbert space established in this work, which may be of independent interest. We further develop an algorithm based on random exploration with domain shrinking and establish its order-optimal regret guarantees under both noise-free and noisy settings. In the noise-free setting, our analysis closes the existing gap in regret performance under a mild assumption on the underlying function and thereby *partially resolves a COLT open problem*. The proposed algorithm also enjoys a computational advantage over prevailing methods due to the random exploration that obviates the expensive optimization of a non-convex acquisition function for choosing the query points at each iteration.

Probabilistic Methods · Bayesian Models and Methods

Luis A. Ortega, Simon Rodriguez Santana, Daniel Hernández-Lobato

The Linearized Laplace Approximation (LLA) has been recently used to perform uncertainty estimation on the predictions of pre-trained deep neural networks (DNNs). However, its widespread application is hindered by significant computational costs, particularly in scenarios with a large number of training points or DNN parameters. Consequently, additional approximations of LLA, such as Kronecker-factored or diagonal approximate GGN matrices, are utilized, potentially compromising the model's performance. To address these challenges, we propose a new method for approximating LLA using a variational sparse Gaussian Process (GP). Our method is based on the dual RKHS formulation of GPs and retains as the predictive mean the output of the original DNN. Furthermore, it allows for efficient stochastic optimization, which results in sub-linear training time in the size of the training dataset. Specifically, its training cost is independent of the number of training points. We compare our proposed method against accelerated LLA (ELLA), which relies on the Nyström approximation, as well as other LLA variants employing the sample-then-optimize principle. Experimental results, both on regression and classification datasets, show that our method outperforms these already existing efficient variants of LLA, both in terms of the quality of the predictive distribution and in terms of total computational time.

Probabilistic Methods · Variational Inference

Xinlei Niu, Christian Walder, Jing Zhang, Charles Martin

We propose the stochastic optimal path which solves the classical optimal path problem by a probability-softening solution. This unified approach transforms a wide range of DP problems into directed acyclic graphs in which all paths follow a Gibbs distribution. We show the equivalence of the Gibbs distribution to a message-passing algorithm by the properties of the Gumbel distribution and give all the ingredients required for variational Bayesian inference of a latent path, namely Bayesian dynamic programming (BDP). We demonstrate the usage of BDP in the latent space of variational autoencoders (VAEs) and propose the BDP-VAE which captures structured sparse optimal paths as latent variables. This enables end-to-end training for generative tasks in which models rely on unobserved structural information. At last, we validate the behavior of our approach and showcase its applicability in two real-world applications: text-to-speech and singing voice synthesis. Our implementation code is available at https://github.com/XinleiNIU/LatentOptimalPathsBayesianDP.

Theory · Domain Adaptation and Transfer Learning

Hossein Zakerinia, Amin Behjati, Christoph Lampert

We introduce a new framework for studying meta-learning methods using PAC-Bayesian theory. Its main advantage over previous work is that it allows for more flexibility in how the transfer of knowledge between tasks is realized. For previous approaches, this could only happen indirectly, by means of learning prior distributions over models. In contrast, the new generalization bounds that we prove express the process of meta-learning much more directly as learning the learning algorithm that should be used for future tasks. The flexibility of our framework makes it suitable to analyze a wide range of meta-learning mechanisms and even design new mechanisms. Other than our theoretical contributions we also show empirically that our framework improves the prediction quality in practical meta-learning mechanisms.

Deep Learning · Large Language Models

JoonHo Lee, Jae Oh Woo, Juree Seok, Parisa Hassanzadeh, Wooseok Jang, JuYoun Son, Sima Didari, Baruch Gutow, Heng Hao, Hankyu Moon 等

Assessing response quality to instructions in language models is vital but challenging due to the complexity of human language across different contexts. This complexity often results in ambiguous or inconsistent interpretations, making accurate assessment difficult. To address this issue, we propose a novel Uncertainty-aware Reward Model (URM) that introduces a robust uncertainty estimation for the quality of paired responses based on Bayesian approximation. Trained with preference datasets, our uncertainty-enabled proxy not only scores rewards for responses but also evaluates their inherent uncertainty. Empirical results demonstrate significant benefits of incorporating the proposed proxy into language model training. Our method boosts the instruction following capability of language models by refining data curation for training and improving policy optimization objectives, thereby surpassing existing methods by a large margin on benchmarks such as Vicuna and MT-bench. These findings highlight that our proposed approach substantially advances language model training and paves a new way of harnessing uncertainty within language models.