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Probabilistic Methods · Variational Inference

Diana Cai, Chirag Modi, Loucas Pillaud-Vivien, Charles Margossian, Robert Gower, David Blei, Lawrence Saul

Most leading implementations of black-box variational inference (BBVI) are based on optimizing a stochastic evidence lower bound (ELBO). But such approaches to BBVI often converge slowly due to the high variance of their gradient estimates and their sensitivity to hyperparameters. In this work, we propose _batch and match_ (BaM), an alternative approach to BBVI based on a score-based divergence. Notably, this score-based divergence can be optimized by a closed-form proximal update for Gaussian variational families with full covariance matrices. We analyze the convergence of BaM when the target distribution is Gaussian, and we prove that in the limit of infinite batch size the variational parameter updates converge exponentially quickly to the target mean and covariance. We also evaluate the performance of BaM on Gaussian and non-Gaussian target distributions that arise from posterior inference in hierarchical and deep generative models. In these experiments, we find that BaM typically converges in fewer (and sometimes significantly fewer) gradient evaluations than leading implementations of BBVI based on ELBO maximization.

Deep Learning · Generative Models and Autoencoders

Beatrix M. G. Nielsen, Anders Christensen, Andrea Dittadi, Ole Winther

Diffusion models may be viewed as hierarchical variational autoencoders (VAEs) with two improvements: parameter sharing for the conditionals in the generative process and efficient computation of the loss as independent terms over the hierarchy. We consider two changes to the diffusion model that retain these advantages while adding flexibility to the model. Firstly, we introduce a data and depth-dependent mean function in the diffusion process, which leads to a modified diffusion loss. Our proposed framework, DiffEnc, achieves a statistically significant improvement in likelihood on CIFAR-10. Secondly, we let the ratio of the noise variance of the reverse encoder process and the generative process be a free weight parameter rather than being fixed to one. This leads to theoretical insights: For a finite depth hierarchy, the evidence lower bound (ELBO) can be used as an objective for a weighted diffusion loss approach and for optimizing the noise schedule specifically for inference. For the infinite-depth hierarchy, on the other hand, the weight parameter has to be one to have a well-defined ELBO.

Probabilistic Methods · Structure Learning

Benjie Wang, Joel Jennings, Wenbo Gong

Discovering the underlying relationships among variables from temporal observations has been a longstanding challenge in numerous scientific disciplines, including biology, finance, and climate science. The dynamics of such systems are often best described using continuous-time stochastic processes. Unfortunately, most existing structure learning approaches assume that the underlying process evolves in discrete-time and/or observations occur at regular time intervals. These mismatched assumptions can often lead to incorrect learned structures and models. In this work, we introduce a novel structure learning method, SCOTCH, which combines neural stochastic differential equations (SDE) with variational inference to infer a posterior distribution over possible structures. This continuous-time approach can naturally handle both learning from and predicting observations at arbitrary time points. Theoretically, we establish sufficient conditions for an SDE and SCOTCH to be structurally identifiable, and prove its consistency under infinite data limits. Empirically, we demonstrate that our approach leads to improved structure learning performance on both synthetic and real-world datasets compared to relevant baselines under regular and irregular sampling intervals.

Probabilistic Methods · Variational Inference

Lorenz Vaitl, Ludwig Winkler, Lorenz Richter, Pan Kessel

Recent work shows that path gradient estimators for normalizing flows have lower variance compared to standard estimators, resulting in improved training. However, they are often prohibitively more expensive from a computational point of view and cannot be applied to maximum likelihood training in a scalable manner, which severely hinders their widespread adoption. In this work, we overcome these crucial limitations. Specifically, we propose a fast path gradient estimator which works for all normalizing flow architectures of practical relevance for sampling from an unnormalized target distribution. We then show that this estimator can also be applied to maximum likelihood training and empirically establish its superior performance for several natural sciences applications.

Probabilistic Methods · Everything Else

Victor Livernoche, Vineet Jain, Yashar Hezaveh, Siamak Ravanbakhsh

Known for their impressive performance in generative modeling, diffusion models are attractive candidates for density-based anomaly detection. This paper investigates different variations of diffusion modeling for unsupervised and semi-supervised anomaly detection. In particular, we find that Denoising Diffusion Probability Models (DDPM) are performant on anomaly detection benchmarks yet computationally expensive. By simplifying DDPM in application to anomaly detection, we are naturally led to an alternative approach called Diffusion Time Estimation (DTE). DTE estimates the distribution over diffusion time for a given input and uses the mode or mean of this distribution as the anomaly score. We derive an analytical form for this density and leverage a deep neural network to improve inference efficiency. Through empirical evaluations on the ADBench benchmark, we demonstrate that all diffusion-based anomaly detection methods perform competitively for both semi-supervised and unsupervised settings. Notably, DTE achieves orders of magnitude faster inference time than DDPM, while outperforming it on this benchmark. These results establish diffusion-based anomaly detection as a scalable alternative to traditional methods and recent deep-learning techniques for standard unsupervised and semi-supervised anomaly detection settings.

Deep Learning · Generative Models and Autoencoders

Morteza Mardani, Jiaming Song, Jan Kautz, Arash Vahdat

Diffusion models have emerged as a key pillar of foundation models in visual domains. One of their critical applications is to universally solve different downstream inverse tasks via a single diffusion prior without re-training for each task. Most inverse tasks can be formulated as inferring a posterior distribution over data (e.g., a full image) given a measurement (e.g., a masked image). This is however challenging in diffusion models since the nonlinear and iterative nature of the diffusion process renders the posterior intractable. To cope with this challenge, we propose a variational approach that by design seeks to approximate the true posterior distribution. We show that our approach naturally leads to regularization by denoising diffusion process (RED-diff) where denoisers at different timesteps concurrently impose different structural constraints over the image. To gauge the contribution of denoisers from different timesteps, we propose a weighting mechanism based on signal-to-noise-ratio (SNR). Our approach provides a new variational perspective for solving inverse problems with diffusion models, allowing us to formulate sampling as stochastic optimization, where one can simply apply off-the-shelf solvers with lightweight iterates. Our experiments for various linear and nonlinear image restoration tasks demonstrate the strengths of our method compared with state-of-the-art sampling-based diffusion models. The code is available online \footnote{\url{https://github.com/NVlabs/RED-diff}}.

Deep Learning · Generative Models and Autoencoders

Khalid OUBLAL, Said Ladjal, David Benhaiem, Emmanuel LE BORGNE, François Roueff

Learning disentangled representations for time series is a promising path to facilitate reliable generalization to in- and out-of distribution (OOD), offering benefits like feature derivation and improved interpretability and fairness, thereby enhancing downstream tasks. We focus on disentangled representation learning for home appliance electricity usage, enabling users to understand and optimize their consumption for a reduced carbon footprint. Our approach frames the problem as disentangling each attribute's role in total consumption. Unlike existing methods assuming attribute independence which leads to non-identiability, we acknowledge real-world time series attribute correlations, learned up to a smooth bijection using contrastive learning and a single autoencoder. To address this, we propose a Disentanglement under Independence-Of-Support via Contrastive Learning (DIOSC), facilitating representation generalization across diverse correlated scenarios. Our method utilizes innovative \textit{l}-variational inference layers with self-attention, effectively addressing temporal dependencies across bottom-up and top-down networks. We find that DIOSC can enhance the task of representation of time series electricity consumption. We introduce TDS (Time Disentangling Score) to gauge disentanglement quality. TDS reliably reflects disentanglement performance, making it a valuable metric for evaluating time series representations disentanglement. Code available at https://institut-polytechnique-de-paris.github.io/time-disentanglement-lib.

Deep Learning · Sequential Models, Time series

Konstantin Hess, Valentyn Melnychuk, Dennis Frauen, Stefan Feuerriegel

Treatment effect estimation in continuous time is crucial for personalized medicine. However, existing methods for this task are limited to point estimates of the potential outcomes, whereas uncertainty estimates have been ignored. Needless to say, uncertainty quantification is crucial for reliable decision-making in medical applications. To fill this gap, we propose a novel Bayesian neural controlled differential equation (BNCDE) for treatment effect estimation in continuous time. In our BNCDE, the time dimension is modeled through a coupled system of neural controlled differential equations and neural stochastic differential equations, where the neural stochastic differential equations allow for tractable variational Bayesian inference. Thereby, for an assigned sequence of treatments, our BNCDE provides meaningful posterior predictive distributions of the potential outcomes. To the best of our knowledge, ours is the first tailored neural method to provide uncertainty estimates of treatment effects in continuous time. As such, our method is of direct practical value for promoting reliable decision-making in medicine.

Applications · Time Series

Hang Yu, Cong Liao, Ruolan Liu, Jianguo Li, Hu Yun, Xinzhe Wang

Periodic patterns are a fundamental characteristic of time series in natural world, with significant implications for a range of disciplines, from economics to cloud systems. However, the current literature on periodicity detection faces two key challenges: limited robustness in real-world scenarios and a lack of memory to leverage previously observed time series to accelerate and improve inference on new data. To overcome these obstacles, this paper presents AmortizedPeriod, an innovative approach to periodicity identification based on amortized variational inference that integrates Bayesian statistics and deep learning. Through the Bayesian generative process, our method flexibly captures the dependencies of the periods, trends, noise, and outliers in time series, while also considering missing data and irregular periods in a robust manner. In addition, it utilizes the evidence lower bound of the log-likelihood of the observed time series as the loss function to train a deep attention inference network, facilitating knowledge transfer from the seen time series (and their labels) to unseen ones. Experimental results show that AmortizedPeriod surpasses the state-of-the-art methods by a large margin of 28.5% on average in terms of micro $F_1$-score, with at least 55% less inference time.

Deep Learning · Other Representation Learning

Ziming Hong, Zhenyi Wang, Li Shen, Yu Yao, Zhuo Huang, Shiming Chen, chuanwu yang, Mingming Gong, Tongliang Liu

Non-transferable learning (NTL) aims to restrict the generalization of models toward the target domain(s). To this end, existing works learn non-transferable representations by reducing statistical dependence between the source and target domain. However, such statistical methods essentially neglect to distinguish between *styles* and *contents*, leading them to inadvertently fit (i) spurious correlation between *styles* and *labels*, and (ii) fake independence between *contents* and *labels*. Consequently, their performance will be limited when natural distribution shifts occur or malicious intervention is imposed. In this paper, we propose a novel method (dubbed as H-NTL) to understand and advance the NTL problem by introducing a causal model to separately model *content* and *style* as two latent factors, based on which we disentangle and harness them as guidances for learning non-transferable representations with intrinsically causal relationships. Specifically, to avoid fitting spurious correlation and fake independence, we propose a variational inference framework to disentangle the naturally mixed *content factors* and *style factors* under our causal model. Subsequently, based on dual-path knowledge distillation, we harness the disentangled two *factors* as guidances for non-transferable representation learning: (i) we constraint the source domain representations to fit *content factors* (which are the intrinsic cause of *labels*), and (ii) we enforce that the target domain representations fit *style factors* which barely can predict labels. As a result, the learned feature representations follow optimal untransferability toward the target domain and minimal negative influence on the source domain, thus enabling better NTL performance. Empirically, the proposed H-NTL significantly outperforms competing methods by a large margin.

James Harrison, John Willes, Jasper Snoek

We introduce a deterministic variational formulation for training Bayesian last layer neural networks. This yields a sampling-free, single-pass model and loss that effectively improves uncertainty estimation. Our variational Bayesian last layer (VBLL) can be trained and evaluated with only quadratic complexity in last layer width, and is thus (nearly) computationally free to add to standard architectures. We experimentally investigate VBLLs, and show that they improve predictive accuracy, calibration, and out of distribution detection over baselines across both regression and classification. Finally, we investigate combining VBLL layers with variational Bayesian feature learning, yielding a lower variance collapsed variational inference method for Bayesian neural networks.

Probabilistic Methods · Variational Inference

Junbo Li, Zichen Miao, Qiang Qiu, Ruqi Zhang

Bayesian neural networks (BNNs) offer uncertainty quantification but come with the downside of substantially increased training and inference costs. Sparse BNNs have been investigated for efficient inference, typically by either slowly introducing sparsity throughout the training or by post-training compression of dense BNNs. The dilemma of how to cut down massive training costs remains, particularly given the requirement to learn about the uncertainty. To solve this challenge, we introduce Sparse Subspace Variational Inference (SSVI), the first fully sparse BNN framework that maintains a consistently sparse Bayesian model throughout the training and inference phases. Starting from a randomly initialized low-dimensional sparse subspace, our approach alternately optimizes the sparse subspace basis selection and its associated parameters. While basis selection is characterized as a non-differentiable problem, we approximate the optimal solution with a removal-and-addition strategy, guided by novel criteria based on weight distribution statistics. Our extensive experiments show that SSVI sets new benchmarks in crafting sparse BNNs, achieving, for instance, a 10-20× compression in model size with under 3\% performance drop, and up to 20× FLOPs reduction during training. Remarkably, SSVI also demonstrates enhanced robustness to hyperparameters, reducing the need for intricate tuning in VI and occasionally even surpassing VI-trained dense BNNs.

Miscellaneous Aspects of Machine Learning · Representation Learning

Shujian Yu, Xi Yu, Sigurd Løkse, Robert Jenssen, Jose Principe

The information bottleneck (IB) approach is popular to improve the generalization, robustness and explainability of deep neural networks. Essentially, it aims to find a minimum sufficient representation $\mathbf{t}$ by striking a trade-off between a compression term $I(\mathbf{x};\mathbf{t})$ and a prediction term $I(y;\mathbf{t})$, where $I(\cdot;\cdot)$ refers to the mutual information (MI). MI is for the IB for the most part expressed in terms of the Kullback-Leibler (KL) divergence, which in the regression case corresponds to prediction based on mean squared error (MSE) loss with Gaussian assumption and compression approximated by variational inference. In this paper, we study the IB principle for the regression problem and develop a new way to parameterize the IB with deep neural networks by exploiting favorable properties of the Cauchy-Schwarz (CS) divergence. By doing so, we move away from MSE-based regression and ease estimation by avoiding variational approximations or distributional assumptions. We investigate the improved generalization ability of our proposed CS-IB and demonstrate strong adversarial robustness guarantees. We demonstrate its superior performance on six real-world regression tasks over other popular deep IB approaches. We additionally observe that the solutions discovered by CS-IB always achieve the best trade-off between prediction accuracy and compression ratio in the information plane. The code is available at \url{https://github.com/SJYuCNEL/Cauchy-Schwarz-Information-Bottleneck}.

Miscellaneous Aspects of Machine Learning · Representation Learning

Kai Lagemann, Christian Lagemann, Sach Mukherjee

We propose a new model class aimed at predicting dynamical trajectories from high-dimensional empirical data. This is done by combining variational autoencoders and (spatio-)temporal transformers within a framework designed to enforce certain scientifically-motivated invariances. The models allow inference of system behavior at any continuous time and generalization well beyond the data distributions seen during training. Furthermore, the models do not require an explicit neural ODE formulation, making them efficient and highly scalable in practice. We study behavior through simple theoretical analyses and extensive empirical experiments. The latter investigate the ability to predict the trajectories of complicated systems based on finite data and show that the proposed approaches can outperform existing neural-dynamical models. We study also more general inductive bias in the context of transfer to data obtained under entirely novel system interventions. Overall, our results provide a new framework for efficiently learning complicated dynamics in a data-driven manner, with potential applications in a wide range of fields including physics, biology, and engineering.

Probabilistic Methods · Variational Inference

Jiajun He, Gergely Flamich, Zongyu Guo, José Miguel Hernández Lobato

COMpression with Bayesian Implicit NEural Representations (COMBINER) is a recent data compression method that addresses a key inefficiency of previous Implicit Neural Representation (INR)-based approaches: it avoids quantization and enables direct optimization of the rate-distortion performance. However, COMBINER still has significant limitations: 1) it uses factorized priors and posterior approximations that lack flexibility; 2) it cannot effectively adapt to local deviations from global patterns in the data; and 3) its performance can be susceptible to modeling choices and the variational parameters' initializations. Our proposed method, Robust and Enhanced COMBINER (RECOMBINER), addresses these issues by 1) enriching the variational approximation while retaining a low computational cost via a linear reparameterization of the INR weights, 2) augmenting our INRs with learnable positional encodings that enable them to adapt to local details and 3) splitting high-resolution data into patches to increase robustness and utilizing expressive hierarchical priors to capture dependency across patches. We conduct extensive experiments across several data modalities, showcasing that RECOMBINER achieves competitive results with the best INR-based methods and even outperforms autoencoder-based codecs on low-resolution images at low bitrates. Our PyTorch implementation is available at https://github.com/cambridge-mlg/RECOMBINER/.

Applications · Neuroscience, Cognitive Science

Chengrui Li, Soon Ho Kim, Chris Rodgers, Hannah Choi, Anqi Wu

Exposing meaningful and interpretable neural interactions is critical to understanding neural circuits. Inferred neural interactions from neural signals primarily reflect functional connectivity. In a long experiment, subject animals may experience different stages defined by the experiment, stimuli, or behavioral states, and hence functional connectivity can change over time. To model dynamically changing functional connectivity, prior work employs state-switching generalized linear models with hidden Markov models (i.e., HMM-GLMs). However, we argue they lack biological plausibility, as functional connectivities are shaped and confined by the underlying anatomical connectome. Here, we propose two novel prior-informed state-switching GLMs, called Gaussian HMM-GLM (Gaussian prior) and one-hot HMM-GLM (Gumbel-Softmax one-hot prior). We show that the learned prior should capture the state-invariant interaction, shedding light on the underlying anatomical connectome and revealing more likely physical neuron interactions. The state-dependent interaction modeled by each GLM offers traceability to capture functional variations across multiple brain states. Our methods effectively recover true interaction structures in simulated data, achieve the highest predictive likelihood, and enhance the interpretability of interaction patterns and hidden states when applied to real neural data. The code is available at \url{https://github.com/JerrySoybean/onehot-hmmglm}.

Applications · Genetics, Cell Biology, etc

MING YANG ZHOU, Zichao Yan, Elliot Layne, Nikolay Malkin, Dinghuai Zhang, Moksh Jain, Mathieu Blanchette, Yoshua Bengio

Phylogenetics is a branch of computational biology that studies the evolutionary relationships among biological entities. Its long history and numerous applications notwithstanding, inference of phylogenetic trees from sequence data remains challenging: the high complexity of tree space poses a significant obstacle for the current combinatorial and probabilistic techniques. In this paper, we adopt the framework of generative flow networks (GFlowNets) to tackle two core problems in phylogenetics: parsimony-based and Bayesian phylogenetic inference. Because GFlowNets are well-suited for sampling complex combinatorial structures, they are a natural choice for exploring and sampling from the multimodal posterior distribution over tree topologies and evolutionary distances. We demonstrate that our amortized posterior sampler, PhyloGFN, produces diverse and high-quality evolutionary hypotheses on real benchmark datasets. PhyloGFN is competitive with prior works in marginal likelihood estimation and achieves a closer fit to the target distribution than state-of-the-art variational inference methods.

Probabilistic Methods · Structure Learning

Aoran Wang, Jun Pang

This paper introduces a novel approach to structural inference, combining a variational dynamics encoder with partial correlation coefficients. In contrast to prior methods, our approach leverages variational inference to encode node dynamics within latent variables, and structural reconstruction relies on the calculation of partial correlation coefficients derived from these latent variables.This unique design endows our method with scalability and extends its applicability to both one-dimensional and multi-dimensional feature spaces.Furthermore, by reorganizing latent variables according to temporal steps, our approach can effectively reconstruct directed graph structures. We validate our method through extensive experimentation on twenty datasets from a benchmark dataset and biological networks. Our results showcase the superior scalability, accuracy, and versatility of our proposed approach compared to existing methods.Moreover, experiments conducted on noisy data affirm the robustness of our method.

Miscellaneous Aspects of Machine Learning · Causality

Ziqi Xu, Debo Cheng, Jiuyong Li, Jixue Liu, Lin Liu, Kui Yu

An essential and challenging problem in causal inference is causal effect estimation from observational data. The problem becomes more difficult with the presence of unobserved confounding variables. The front-door adjustment is an approach for dealing with unobserved confounding variables. However, the restriction for the standard front-door adjustment is difficult to satisfy in practice. In this paper, we relax some of the restrictions by proposing the concept of conditional front-door (CFD) adjustment and develop the theorem that guarantees the causal effect identifiability of CFD adjustment. By leveraging the ability of deep generative models, we propose CFDiVAE to learn the representation of the CFD adjustment variable directly from data with the identifiable Variational AutoEncoder and formally prove the model identifiability. Extensive experiments on synthetic datasets validate the effectiveness of CFDiVAE and its superiority over existing methods. The experiments also show that the performance of CFDiVAE is less sensitive to the causal strength of unobserved confounding variables. We further apply CFDiVAE to a real-world dataset to demonstrate its potential application.

Social Aspects · Privacy-preserving Statistics and Machine Learning

Mingkun Yang, Ran Zhu, Qing Wang, Jie Yang

Federated Learning (FL) is an important privacy-preserving learning paradigm that plays an important role in the Intelligent Internet of Things. Training a global model in FL, however, is vulnerable to the noise in the heterogeneous data across the clients. In this paper, we introduce **FedTrans**, a novel client-transparent client utility estimation method designed to guide client selection for noisy scenarios, mitigating performance degradation problems. To estimate the client utility, we propose a Bayesian framework that models client utility and its relationships with the weight parameters and the performance of local models. We then introduce a variational inference algorithm to effectively infer client utility, given only a small amount of auxiliary data. Our evaluation demonstrates that leveraging FedTrans as a guide for client selection can lead to a better accuracy performance (up to 7.8\%), ensuring robustness in noisy scenarios.