论文检索

Probabilistic Methods/Bayesian Models and Methods

Florian Seligmann, Philipp Becker, Michael Volpp, Gerhard Neumann

Bayesian deep learning (BDL) is a promising approach to achieve well-calibrated predictions on distribution-shifted data. Nevertheless, there exists no large-scale survey that evaluates recent SOTA methods on diverse, realistic, and challenging benchmark tasks in a systematic manner. To provide a clear picture of the current state of BDL research, we evaluate modern BDL algorithms on real-world datasets from the WILDS collection containing challenging classification and regression tasks, with a focus on generalization capability and calibration under distribution shift. We compare the algorithms on a wide range of large, convolutional and transformer-based neural network architectures. In particular, we investigate a signed version of the expected calibration error that reveals whether the methods are over- or underconfident, providing further insight into the behavior of the methods. Further, we provide the first systematic evaluation of BDL for fine-tuning large pre-trained models, where training from scratch is prohibitively expensive. Finally, given the recent success of Deep Ensembles, we extend popular single-mode posterior approximations to multiple modes by the use of ensembles. While we find that ensembling single-mode approximations generally improves the generalization capability and calibration of the models by a significant margin, we also identify a failure mode of ensembles when finetuning large transformer-based language models. In this setting, variational inference based approaches such as last-layer Bayes By Backprop outperform other methods in terms of accuracy by a large margin, while modern approximate inference algorithms such as SWAG achieve the best calibration.

Applications/Genetics, Cell Biology, etc

Takahiro Mimori, Michiaki Hamada

Phylogenetic inference, grounded in molecular evolution models, is essential for understanding the evolutionary relationships in biological data. Accounting for the uncertainty of phylogenetic tree variables, which include tree topologies and evolutionary distances on branches, is crucial for accurately inferring species relationships from molecular data and tasks requiring variable marginalization. Variational Bayesian methods are key to developing scalable, practical models; however, it remains challenging to conduct phylogenetic inference without restricting the combinatorially vast number of possible tree topologies. In this work, we introduce a novel, fully differentiable formulation of phylogenetic inference that leverages a unique representation of topological distributions in continuous geometric spaces. Through practical considerations on design spaces and control variates for gradient estimations, our approach, GeoPhy, enables variational inference without limiting the topological candidates. In experiments using real benchmark datasets, GeoPhy significantly outperformed other approximate Bayesian methods that considered whole topologies.

Probabilistic Methods/Monte Carlo and Sampling Methods

Louis Sharrock, Lester Mackey, Christopher Nemeth

We introduce a suite of new particle-based algorithms for sampling in constrained domains which are entirely learning rate free. Our approach leverages coin betting ideas from convex optimisation, and the viewpoint of constrained sampling as a mirrored optimisation problem on the space of probability measures. Based on this viewpoint, we also introduce a unifying framework for several existing constrained sampling algorithms, including mirrored Langevin dynamics and mirrored Stein variational gradient descent. We demonstrate the performance of our algorithms on a range of numerical examples, including sampling from targets on the simplex, sampling with fairness constraints, and constrained sampling problems in post-selection inference. Our results indicate that our algorithms achieve competitive performance with existing constrained sampling methods, without the need to tune any hyperparameters.

Probabilistic Methods/Variational Inference

Zongyu Guo, Gergely Flamich, Jiajun He, Zhibo Chen, José Miguel Hernández-Lobato

Many common types of data can be represented as functions that map coordinates to signal values, such as pixel locations to RGB values in the case of an image. Based on this view, data can be compressed by overfitting a compact neural network to its functional representation and then encoding the network weights. However, most current solutions for this are inefficient, as quantization to low-bit precision substantially degrades the reconstruction quality. To address this issue, we propose overfitting variational Bayesian neural networks to the data and compressing an approximate posterior weight sample using relative entropy coding instead of quantizing and entropy coding it. This strategy enables direct optimization of the rate-distortion performance by minimizing the $\beta$-ELBO, and target different rate-distortion trade-offs for a given network architecture by adjusting $\beta$. Moreover, we introduce an iterative algorithm for learning prior weight distributions and employ a progressive refinement process for the variational posterior that significantly enhances performance. Experiments show that our method achieves strong performance on image and audio compression while retaining simplicity.

Optimization/Sampling and Optimization

Aniket Das, Dheeraj Nagaraj

Stein Variational Gradient Descent (SVGD) is a popular particle-based variational inference algorithm with impressive empirical performance across various domains. Although the population (i.e, infinite-particle) limit dynamics of SVGD is well characterized, its behavior in the finite-particle regime is far less understood. To this end, our work introduces the notion of *virtual particles* to develop novel stochastic approximations of population-limit SVGD dynamics in the space of probability measures, that are exactly realizable using finite particles. As a result, we design two computationally efficient variants of SVGD, namely VP-SVGD and GB-SVGD, with provably fast finite-particle convergence rates. Our algorithms can be viewed as specific random-batch approximations of SVGD, which are computationally more efficient than ordinary SVGD. We show that the $n$ particles output by VP-SVGD and GB-SVGD, run for $T$ steps with batch-size $K$, are at-least as good as i.i.d samples from a distribution whose Kernel Stein Discrepancy to the target is at most $O(\tfrac{d^{1/3}}{(KT)^{1/6}})$ under standard assumptions. Our results also hold under a mild growth condition on the potential function, which is much weaker than the isoperimetric (e.g. Poincare Inequality) or information-transport conditions (e.g. Talagrand's Inequality $\mathsf{T}_1$) generally considered in prior works. As a corollary, we analyze the convergence of the empirical measure (of the particles output by VP-SVGD and GB-SVGD) to the target distribution and demonstrate a **double exponential improvement** over the best known finite-particle analysis of SVGD. Beyond this, our results present the **first known oracle complexities for this setting with polynomial dimension dependence**, thereby completely eliminating the curse of dimensionality exhibited by previously known finite-particle rates.

Social Aspects/Privacy-preserving Statistics and Machine Learning

Pratik Karmakar, Debabrota Basu

We study design of black-box model extraction attacks that can *send minimal number of queries from* a *publicly available dataset* to a target ML model through a predictive API with an aim *to create an informative and distributionally equivalent replica* of the target.First, we define *distributionally equivalent* and *Max-Information model extraction* attacks, and reduce them into a variational optimisation problem. The attacker sequentially solves this optimisation problem to select the most informative queries that simultaneously maximise the entropy and reduce the mismatch between the target and the stolen models. This leads to *an active sampling-based query selection algorithm*, Marich, which is *model-oblivious*. Then, we evaluate Marich on different text and image data sets, and different models, including CNNs and BERT. Marich extracts models that achieve $\sim 60-95\%$ of true model's accuracy and uses $\sim 1,000 - 8,500$ queries from the publicly available datasets, which are different from the private training datasets. Models extracted by Marich yield prediction distributions, which are $\sim2-4\times$ closer to the target's distribution in comparison to the existing active sampling-based attacks. The extracted models also lead to 84-96$\%$ accuracy under membership inference attacks. Experimental results validate that Marich is *query-efficient*, and capable of performing task-accurate, high-fidelity, and informative model extraction.

Applications/Neuroscience, Cognitive Science

Yizi Zhang, Tianxiao He, Julien Boussard, Charles Windolf, Olivier Winter, Eric Trautmann, Noam Roth, Hailey Barrell, Mark Churchland, Nicholas A Steinmetz 等

Neural decoding and its applications to brain computer interfaces (BCI) are essential for understanding the association between neural activity and behavior. A prerequisite for many decoding approaches is spike sorting, the assignment of action potentials (spikes) to individual neurons. Current spike sorting algorithms, however, can be inaccurate and do not properly model uncertainty of spike assignments, therefore discarding information that could potentially improve decoding performance. Recent advances in high-density probes (e.g., Neuropixels) and computational methods now allow for extracting a rich set of spike features from unsorted data; these features can in turn be used to directly decode behavioral correlates. To this end, we propose a spike sorting-free decoding method that directly models the distribution of extracted spike features using a mixture of Gaussians (MoG) encoding the uncertainty of spike assignments, without aiming to solve the spike clustering problem explicitly. We allow the mixing proportion of the MoG to change over time in response to the behavior and develop variational inference methods to fit the resulting model and to perform decoding. We benchmark our method with an extensive suite of recordings from different animals and probe geometries, demonstrating that our proposed decoder can consistently outperform current methods based on thresholding (i.e. multi-unit activity) and spike sorting. Open source code is available at https://github.com/yzhang511/density_decoding.

Miscellaneous Aspects of Machine Learning

Jun-Yi Hang, Min-Ling Zhang

In partial multi-label learning (PML), each training example is associated with a set of candidate labels, among which only some labels are valid. As a common strategy to tackle PML problem, disambiguation aims to recover the ground-truth labeling information from such inaccurate annotations. However, existing approaches mainly rely on heuristics or ad-hoc rules to disambiguate candidate labels, which may not be universal enough in complicated real-world scenarios. To provide a principled way for disambiguation, we make a first attempt to explore the probabilistic graphical model for PML problem, where a directed graph is tailored to infer latent ground-truth labeling information from the generative process of partial multi-label data. Under the framework of stochastic gradient variational Bayes, a unified variational lower bound is derived for this graphical model, which is further relaxed probabilistically so that the desired prediction model can be induced with simultaneously identified ground-truth labeling information. Comprehensive experiments on multiple synthetic and real-world data sets show that our approach outperforms the state-of-the-art counterparts.

Probabilistic Methods/Variational Inference

Veit David Wild, Sahra Ghalebikesabi, Dino Sejdinovic, Jeremias Knoblauch

We establish the first mathematically rigorous link between Bayesian, variational Bayesian, and ensemble methods. A key step towards this it to reformulate the non-convex optimisation problem typically encountered in deep learning as a convex optimisation in the space of probability measures. On a technical level, our contribution amounts to studying generalised variational inference through the lense of Wasserstein gradient flows. The result is a unified theory of various seemingly disconnected approaches that are commonly used for uncertainty quantification in deep learning---including deep ensembles and (variational) Bayesian methods. This offers a fresh perspective on the reasons behind the success of deep ensembles over procedures based on parameterised variational inference, and allows the derivation of new ensembling schemes with convergence guarantees. We showcase this by proposing a family of interacting deep ensembles with direct parallels to the interactions of particle systems in thermodynamics, and use our theory to prove the convergence of these algorithms to a well-defined global minimiser on the space of probability measures.

Probabilistic Methods

Sebastian Salazar

Decision trees are a well-established tool in machine learning for classification and regression tasks. In this paper, we introduce a novel non-parametric Bayesian model that uses variational inference to approximate a posterior distribution over the space of stochastic decision trees. We evaluate the model's performance on 18 datasets and demonstrate its competitiveness with other state-of-the-art methods in regression tasks. We also explore its application to causal inference problems. We provide a fully vectorized implementation of our algorithm in PyTorch.

Probabilistic Methods/Variational Inference

Justin Domke, Robert Gower, Guillaume Garrigos

Black-box variational inference is widely used in situations where there is no proof that its stochastic optimization succeeds. We suggest this is due to a theoretical gap in existing stochastic optimization proofs—namely the challenge of gradient estimators with unusual noise bounds, and a composite non-smooth objective. For dense Gaussian variational families, we observe that existing gradient estimators based on reparameterization satisfy a quadratic noise bound and give novel convergence guarantees for proximal and projected stochastic gradient descent using this bound. This provides rigorous guarantees that methods similar to those used in practice converge on realistic inference problems.

Deep Learning/Generative Models and Autoencoders

Paribesh Regmi, Rui Li

The neural network structures of generative models and their corresponding inference models paired in variational autoencoders (VAEs) play a critical role in the models' generative performance. However, powerful VAE network structures are hand-crafted and fixed prior to training, resulting in a one-size-fits-all approach that requires heavy computation to tune for given data. Moreover, existing VAE regularization methods largely overlook the importance of network structures and fail to prevent overfitting in deep VAE models with cascades of hidden layers. To address these issues, we propose a Bayesian inference framework that automatically adapts VAE network structures to data and prevent overfitting as they grow deeper. We model the number of hidden layers with a beta process to infer the most plausible encoding/decoding network depths warranted by data and perform layer-wise dropout regularization with a conjugate Bernoulli process. We develop a scalable estimator that performs joint inference on both VAE network structures and latent variables. Our experiments show that the inference framework effectively prevents overfitting in both shallow and deep VAE models, yielding state-of-the-art performance. We demonstrate that our framework is compatible with different types of VAE backbone networks and can be applied to various VAE variants, further improving their performance.

Applications/Physics

Xiao Luo, Haixin Wang, Zijie Huang, Huiyu Jiang, Abhijeet Gangan, Song Jiang, Yizhou Sun

Modeling interacting dynamical systems, such as fluid dynamics and intermolecular interactions, is a fundamental research problem for understanding and simulating complex real-world systems. Many of these systems can be naturally represented by dynamic graphs, and graph neural network-based approaches have been proposed and shown promising performance. However, most of these approaches assume the underlying dynamics does not change over time, which is unfortunately untrue. For example, a molecular dynamics can be affected by the environment temperature over the time. In this paper, we take an attempt to provide a probabilistic view for time-varying dynamics and propose a model Context-attended Graph ODE (CARE) for modeling time-varying interacting dynamical systems. In our CARE, we explicitly use a context variable to model time-varying environment and construct an encoder to initialize the context variable from historical trajectories. Furthermore, we employ a neural ODE model to depict the dynamic evolution of the context variable inferred from system states. This context variable is incorporated into a coupled ODE to simultaneously drive the evolution of systems. Comprehensive experiments on four datasets demonstrate the effectiveness of our proposed CARE compared with several state-of-the-art approaches.

Probabilistic Methods/Variational Inference

Kevin Course, Prasanth Nair

We consider the problem of inferring latent stochastic differential equations (SDEs) with a time and memory cost that scales independently with the amount of data, the total length of the time series, and the stiffness of the approximate differential equations. This is in stark contrast to typical methods for inferring latent differential equations which, despite their constant memory cost, have a time complexity that is heavily dependent on the stiffness of the approximate differential equation. We achieve this computational advancement by removing the need to solve differential equations when approximating gradients using a novel amortization strategy coupled with a recently derived reparametrization of expectations under linear SDEs. We show that, in practice, this allows us to achieve similar performance to methods based on adjoint sensitivities with more than an order of magnitude fewer evaluations of the model in training.

Deep Learning/Generative Models and Autoencoders

Laura Manduchi, Moritz Vandenhirtz, Alain Ryser, Julia Vogt

We propose Tree Variational Autoencoder (TreeVAE), a new generative hierarchical clustering model that learns a flexible tree-based posterior distribution over latent variables. TreeVAE hierarchically divides samples according to their intrinsic characteristics, shedding light on hidden structures in the data. It adapts its architecture to discover the optimal tree for encoding dependencies between latent variables. The proposed tree-based generative architecture enables lightweight conditional inference and improves generative performance by utilizing specialized leaf decoders. We show that TreeVAE uncovers underlying clusters in the data and finds meaningful hierarchical relations between the different groups on a variety of datasets, including real-world imaging data. We present empirically that TreeVAE provides a more competitive log-likelihood lower bound than the sequential counterparts. Finally, due to its generative nature, TreeVAE is able to generate new samples from the discovered clusters via conditional sampling.

Probabilistic Methods/Graphical Models

Fiona Lippert, Bart Kranstauber, Emiel van Loon, Patrick Forré

Probabilistic inference in high-dimensional state-space models is computationally challenging. For many spatiotemporal systems, however, prior knowledge about the dependency structure of state variables is available. We leverage this structure to develop a computationally efficient approach to state estimation and learning in graph-structured state-space models with (partially) unknown dynamics and limited historical data. Building on recent methods that combine ideas from deep learning with principled inference in Gaussian Markov random fields (GMRF), we reformulate graph-structured state-space models as Deep GMRFs defined by simple spatial and temporal graph layers. This results in a flexible spatiotemporal prior that can be learned efficiently from a single time sequence via variational inference. Under linear Gaussian assumptions, we retain a closed-form posterior, which can be sampled efficiently using the conjugate gradient method, scaling favourably compared to classical Kalman filter based approaches.

Probabilistic Methods/Variational Inference

Tianle Liu, Promit Ghosal, Krishnakumar Balasubramanian, Natesh Pillai

Stein Variational Gradient Descent (SVGD) is a nonparametric particle-based deterministic sampling algorithm. Despite its wide usage, understanding the theoretical properties of SVGD has remained a challenging problem. For sampling from a Gaussian target, the SVGD dynamics with a bilinear kernel will remain Gaussian as long as the initializer is Gaussian. Inspired by this fact, we undertake a detailed theoretical study of the Gaussian-SVGD, i.e., SVGD projected to the family of Gaussian distributions via the bilinear kernel, or equivalently Gaussian variational inference (GVI) with SVGD. We present a complete picture by considering both the mean-field PDE and discrete particle systems. When the target is strongly log-concave, the mean-field Gaussian-SVGD dynamics is proven to converge linearly to the Gaussian distribution closest to the target in KL divergence. In the finite-particle setting, there is both uniform in time convergence to the mean-field limit and linear convergence in time to the equilibrium if the target is Gaussian. In the general case, we propose a density-based and a particle-based implementation of the Gaussian-SVGD, and show that several recent algorithms for GVI, proposed from different perspectives, emerge as special cases of our unified framework. Interestingly, one of the new particle-based instance from this framework empirically outperforms existing approaches. Our results make concrete contributions towards obtaining a deeper understanding of both SVGD and GVI.

Probabilistic Methods/Variational Inference

Prateek Jaiswal, Harsha Honnappa, Vinayak Rao

We study data-driven decision-making problems in the Bayesian framework, where the expectation in the Bayes risk is replaced by a risk-sensitive entropic risk measure with respect to the posterior distribution. We focus on problems where calculating the posterior distribution is intractable, a typical situation in modern applications with large datasets and complex data generating models. We leverage a dual representation of the entropic risk measure to introduce a novel risk-sensitive variational Bayesian (RSVB) framework for jointly computing a risk-sensitive posterior approximation and the corresponding decision rule. Our general framework includes \textit{loss-calibrated} VB (Lacoste-Julien et al. [2011] ) as a special case. We also study the impact of these computational approximations on the predictive performance of the inferred decision rules. We compute the convergence rates of the RSVB approximate posterior and the corresponding optimal value. We illustrate our theoretical findings in parametric and nonparametric settings with the help of three examples.

Applications/Computer Vision

Changsheng Lv, Shuai Zhang, Yapeng Tian, Mengshi Qi, Huadong Ma

In this paper, we propose a Disentangled Counterfactual Learning (DCL) approach for physical audiovisual commonsense reasoning. The task aims to infer objects’ physics commonsense based on both video and audio input, with the main challenge is how to imitate the reasoning ability of humans. Most of the current methods fail to take full advantage of different characteristics in multi-modal data, and lacking causal reasoning ability in models impedes the progress of implicit physical knowledge inferring. To address these issues, our proposed DCL method decouples videos into static (time-invariant) and dynamic (time-varying) factors in the latent space by the disentangled sequential encoder, which adopts a variational autoencoder (VAE) to maximize the mutual information with a contrastive loss function. Furthermore, we introduce a counterfactual learning module to augment the model’s reasoning ability by modeling physical knowledge relationships among different objects under counterfactual intervention. Our proposed method is a plug-and-play module that can be incorporated into any baseline. In experiments, we show that our proposed method improves baseline methods and achieves state-of-the-art performance. Our source code is available at https://github.com/Andy20178/DCL.

Probabilistic Methods/Bayesian Models and Methods

Longlin Yu, Tianyu Xie, Yu Zhu, Tong Yang, Xiangyu Zhang, Cheng Zhang

Semi-implicit variational inference (SIVI) has been introduced to expand the analytical variational families by defining expressive semi-implicit distributions in a hierarchical manner. However, the single-layer architecture commonly used in current SIVI methods can be insufficient when the target posterior has complicated structures. In this paper, we propose hierarchical semi-implicit variational inference, called HSIVI, which generalizes SIVI to allow more expressive multi-layer construction of semi-implicit distributions. By introducing auxiliary distributions that interpolate between a simple base distribution and the target distribution, the conditional layers can be trained by progressively matching these auxiliary distributions one layer after another. Moreover, given pre-trained score networks, HSIVI can be used to accelerate the sampling process of diffusion models with the score matching objective. We show that HSIVI significantly enhances the expressiveness of SIVI on several Bayesian inference problems with complicated target distributions. When used for diffusion model acceleration, we show that HSIVI can produce high quality samples comparable to or better than the existing fast diffusion model based samplers with a small number of function evaluations on various datasets.