In the last years, the weakly supervised paradigm of multiple instance learning (MIL) has become very popular in many different areas. A paradigmatic example is computational pathology, where the lack of patch-level labels for whole-slide images prevents the application of supervised models. Probabilistic MIL methods based on Gaussian Processes (GPs) have obtained promising results due to their excellent uncertainty estimation capabilities. However, these are general-purpose MIL methods that do not take into account one important fact: in (histopathological) images, the labels of neighboring patches are expected to be correlated. In this work, we extend a state-of-the-art GP-based MIL method, which is called VGPMIL-PR, to exploit such correlation. To do so, we develop a novel coupling term inspired by the statistical physics Ising model. We use variational inference to estimate all the model parameters. Interestingly, the VGPMIL-PR formulation is recovered when the weight that regulates the strength of the Ising term vanishes. The performance of the proposed method is assessed in two real-world problems of prostate cancer detection. We show that our model achieves better results than other state-of-the-art probabilistic MIL methods. We also provide different visualizations and analysis to gain insights into the influence of the novel Ising term. These insights are expected to facilitate the application of the proposed model to other research areas.
Machine learning applications for longitudinal electronic health records often forecast the risk of events at fixed time points, whereas survival analysis achieves dynamic risk prediction by estimating time-to-event distributions. Here, we propose a novel conditional variational autoencoder-based method, DySurv, which uses a combination of static and longitudinal measurements from electronic health records to estimate the individual risk of death dynamically. DySurv directly estimates the cumulative risk incidence function without making any parametric assumptions on the underlying stochastic process of the time-to-event. We evaluate DySurv on 6 time-to-event benchmark datasets in healthcare, as well as 2 real-world intensive care unit (ICU) electronic health records (EHR) datasets extracted from the eICU Collaborative Research (eICU) and the Medical Information Mart for Intensive Care database (MIMIC-IV). DySurv outperforms other existing statistical and deep learning approaches to time-to-event analysis across concordance and other metrics. It achieves time-dependent concordance of over 60% in the eICU case. It is also over 12% more accurate and 22% more sensitive than in-use ICU scores like Acute Physiology and Chronic Health Evaluation (APACHE) and Sequential Organ Failure Assessment (SOFA) scores. The predictive capacity of DySurv is consistent and the survival estimates remain disentangled across different datasets. Our interdisciplinary framework successfully incorporates deep learning, survival analysis, and intensive care to create a novel method for time-to-event prediction from longitudinal health records. We test our method on several held-out test sets from a variety of healthcare datasets and compare it to existing in-use clinical risk scoring benchmarks.
Transformed Gaussian Processes (TGPs) are stochastic processes specified by transforming samples from the joint distribution from a prior process (typically a GP) using an invertible transformation; increasing the flexibility of the base process. Furthermore, they achieve competitive results compared with Deep Gaussian Processes (DGPs), which are another generalization constructed by a hierarchical concatenation of GPs. In this work, we propose a generalization of TGPs named Deep Transformed Gaussian Processes (DTGPs), which follows the trend of concatenating layers of stochastic processes. More precisely, we obtain a multi-layer model in which each layer is a TGP. This generalization implies an increment of flexibility with respect to both TGPs and DGPs. Exact inference in such a model is intractable. However, we show that one can use variational inference to approximate the required computations yielding a straightforward extension of the popular DSVI inference algorithm Salimbeni et al (2017). The experiments conducted evaluate the proposed novel DTGPs in multiple regression datasets, achieving good scalability and performance.
Generative diffusion models have achieved spectacular performance in many areas of machine learning and generative modeling. While the fundamental ideas behind these models come from non-equilibrium physics, variational inference and stochastic calculus, in this paper we show that many aspects of these models can be understood using the tools of equilibrium statistical mechanics. Using this reformulation, we show that generative diffusion models undergo second-order phase transitions corresponding to symmetry breaking phenomena. We show that these phase-transitions are always in a mean-field universality class, as they are the result of a self-consistency condition in the generative dynamics. We argue that the critical instability that arises from the phase transitions lies at the heart of their generative capabilities, which are characterized by a set of mean-field critical exponents. Finally, we show that the dynamic equation of the generative process can be interpreted as a stochastic adiabatic transformation that minimizes the free energy while keeping the system in thermal equilibrium.
Spiking neural networks (SNNs) are recurrent models that can leverage sparsity in input time series to efficiently carry out tasks such as classification. Additional efficiency gains can be obtained if decisions are taken as early as possible as a function of the complexity of the input time series. The decision on when to stop inference and produce a decision must rely on an estimate of the current accuracy of the decision. Prior work demonstrated the use of conformal prediction (CP) as a principled way to quantify uncertainty and support adaptive-latency decisions in SNNs. In this paper, we propose to enhance the uncertainty quantification capabilities of SNNs by implementing ensemble models for the purpose of improving the reliability of stopping decisions. Intuitively, an ensemble of multiple models can decide when to stop more reliably by selecting times at which most models agree that the current accuracy level is sufficient. The proposed method relies on different forms of information pooling from ensemble models, and offers theoretical reliability guarantees. We specifically show that variational inference-based ensembles with p-variable pooling significantly reduce the average latency of state-of-the-art methods, while maintaining reliability guarantees.
Adaptive importance sampling (AIS) algorithms are widely used to approximate expectations with respect to complicated target probability distributions. When the target has heavy tails, existing AIS algorithms can provide inconsistent estimators or exhibit slow convergence, as they often neglect the target's tail behaviour. To avoid this pitfall, we propose an AIS algorithm that approximates the target by Student-t proposal distributions. We adapt location and scale parameters by matching the escort moments - which are defined even for heavy-tailed distributions - of the target and the proposal. These updates minimize the $\alpha$-divergence between the target and the proposal, thereby connecting with variational inference. We then show that the $\alpha$-divergence can be approximated by a generalized notion of effective sample size and leverage this new perspective to adapt the tail parameter with Bayesian optimization. We demonstrate the efficacy of our approach through applications to synthetic targets and a Bayesian Student-t regression task on a real example with clinical trial data.
Variational inference (VI) can be cast as an optimization problem in which the variational parameters are tuned to closely align a variational distribution with the true posterior. The optimization task can be approached through vanilla gradient descent in black-box VI or natural-gradient descent in natural-gradient VI. In this work, we reframe VI as the optimization of an objective that concerns probability distributions defined over a \textit{variational parameter space}. Subsequently, we propose Wasserstein gradient descent for tackling this optimization problem. Notably, the optimization techniques, namely black-box VI and natural-gradient VI, can be reinterpreted as specific instances of the proposed Wasserstein gradient descent. To enhance the efficiency of optimization, we develop practical methods for numerically solving the discrete gradient flows. We validate the effectiveness of the proposed methods through empirical experiments on a synthetic dataset, supplemented by theoretical analyses.
Domain invariant learning aims to learn models that extract invariant features over various training domains, resulting in better generalization to unseen target domains. Recently, Bayesian Neural Networks have achieved promising results in domain invariant learning, but most works concentrate on aligning features distributions rather than parameter distributions. Inspired by the principle of Bayesian Neural Network, we attempt to directly learn the domain invariant posterior distribution of network parameters. We first propose a theorem to show that the invariant posterior of parameters can be implicitly inferred by aggregating posteriors on different training domains. Our assumption is more relaxed and allows us to extract more domain invariant information. We also propose a simple yet effective method, named PosTerior Generalization (PTG), that can be used to estimate the invariant parameter distribution. PTG fully exploits variational inference to approximate parameter distributions, including the invariant posterior and the posteriors on training domains. Furthermore, we develop a lite version of PTG for widespread applications. PTG shows competitive performance on various domain generalization benchmarks on DomainBed. Additionally, PTG can use any existing domain generalization methods as its prior, and combined with previous state-of-the-art method the performance can be further improved. Code will be made public.
This work aims efficiently estimating the posterior distribution of kinetic parameters for dynamic positron emission tomography (PET) imaging given a measurement of time of activity curve. Considering the inherent information loss from parametric imaging to measurement space with the forward kinetic model, the inverse mapping is ambiguous. The conventional (but expensive) solution can be the Markov Chain Monte Carlo (MCMC) sampling, which is known to produce unbiased asymptotical estimation. We propose a deep-learning-based framework for efficient posterior estimation. Specifically, we counteract the information loss in the forward process by introducing latent variables. Then, we use a conditional variational autoencoder (CVAE) and optimize its evidence lower bound. The well-trained decoder is able to infer the posterior with a given measurement and the sampled latent variables following a simple multivariate Gaussian distribution. We validate our CVAE-based method using unbiased MCMC as the reference for low-dimensional data (a single brain region) with the simplified reference tissue model.
Onsite disasters like earthquakes can trigger cascading hazards and impacts, such as landslides and infrastructure damage, leading to catastrophic losses; thus, rapid and accurate estimates are crucial for timely and effective post-disaster responses. Interferometric Synthetic aperture radar (InSAR) data is important in providing high-resolution onsite information for rapid hazard estimation. Most recent methods using InSAR imagery signals predict a single type of hazard and thus often suffer low accuracy due to noisy and complex signals induced by co-located hazards, impacts, and irrelevant environmental changes (e.g., vegetation changes, human activities). We introduce a novel stochastic variational inference with normalizing flows derived to jointly approximate posteriors of multiple unobserved hazards and impacts from noisy InSAR imagery.
We present a novel variational framework for performing inference in (neural) stochastic differential equations (SDEs) driven by Markov-approximate fractional Brownian motion (fBM). SDEs offer a versatile tool for modeling real-world continuous-time dynamic systems with inherent noise and randomness. Combining SDEs with the powerful inference capabilities of variational methods, enables the learning of representative function distributions through stochastic gradient descent. However, conventional SDEs typically assume the underlying noise to follow a Brownian motion (BM), which hinders their ability to capture long-term dependencies. In contrast, fractional Brownian motion (fBM) extends BM to encompass non-Markovian dynamics, but existing methods for inferring fBM parameters are either computationally demanding or statistically inefficient. In this paper, building upon the Markov approximation of fBM, we derive the evidence lower bound essential for efficient variational inference of posterior path measures, drawing from the well-established field of stochastic analysis. Additionally, we provide a closed-form expression to determine optimal approximation coefficients. Furthermore, we propose the use of neural networks to learn the drift, diffusion and control terms within our variational posterior, leading to the variational training of neural-SDEs. In this framework, we also optimize the Hurst index, governing the nature of our fractional noise. Beyond validation on synthetic data, we contribute a novel architecture for variational latent video prediction,-an approach that, to the best of our knowledge, enables the first variational neural-SDE application to video perception.
Natural gradient methods have been used to optimise the parameters of probability distributions in a variety of settings, often resulting in fast-converging procedures. Unfortunately, for many distributions of interest, computing the natural gradient has a number of challenges. In this work we propose a novel technique for tackling such issues, which involves reframing the optimisation as one with respect to the parameters of a surrogate distribution, for which computing the natural gradient is easy. We give several examples of existing methods that can be interpreted as applying this technique, and propose a new method for applying it to a wide variety of problems. Our method expands the set of distributions that can be efficiently targeted with natural gradients. Furthermore, it is fast, easy to understand, simple to implement using standard autodiff software, and does not require lengthy model-specific derivations. We demonstrate our method on maximum likelihood estimation and variational inference tasks.
Self-Supervised Learning (SSL) has shown significant potential and has garnered increasing interest in graph learning. However, particularly for generative SSL methods, its potential in Heterogeneous Graph Learning (HGL) remains relatively underexplored. Generative SSL utilizes an encoder to map the input graph into a latent representation and a decoder to recover the input graph from the latent representation. Previous HGL SSL methods generally design complex strategies to capture graph heterogeneity, which heavily rely on contrastive view construction strategies that are often non-trivial. Yet, refining the latent representation in generative SSL can effectively improve graph learning results. In this study, we propose HGVAE, a generative SSL method specially designed for HGL. Instead of focusing on designing complex strategies to capture heterogeneity, HGVAE centers on refining the latent representation. Specifically, HGVAE innovatively develops a contrastive task based on the latent representation. To ensure the hardness of negative samples, we develop a progressive negative sample generation (PNSG) mechanism that leverages the ability of Variational Inference (VI) to generate high-quality negative samples. As a pioneer in applying generative SSL for HGL, HGVAE refines the latent representation, thereby compelling the model to learn high-quality representations. Compared with various state-of-the-art (SOTA) baselines, HGVAE achieves impressive results, thus validating its superiority.
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. Our code is available at https://github.com/zmy1116/phylogfn.
Discovering causal relationships from time series data is significant in fields such as finance, climate science, and neuroscience. However, contemporary techniques rely on the simplifying assumption that data originates from the same causal model, while in practice, data is heterogeneous and can stem from different causal models. In this work, we relax this assumption and perform causal discovery from time series data originating from a mixture of causal models. We propose a general variational inference-based framework called MCD to infer the underlying causal models as well as the mixing probability of each sample. Our approach employs an end-to-end training process that maximizes an evidence-lower bound for the data likelihood. We present two variants: MCD-Linear for linear relationships and independent noise, and MCD-Nonlinear for nonlinear causal relationships and history-dependent noise. We demonstrate that our method surpasses state-of-the-art benchmarks in causal discovery tasks through extensive experimentation on synthetic and real-world datasets, particularly when the data emanates from diverse underlying causal graphs. Theoretically, we prove the identifiability of such a model under some mild assumptions.
Backdoor adjustment is a technique in causal inference for estimating interventional quantities from purely observational data. For example, in medical settings, backdoor adjustment can be used to control for confounding and estimate the effectiveness of a treatment. However, high dimensional treatments and confounders pose a series of potential pitfalls: tractability, identifiability, optimization. In this work, we take a generative modeling approach to backdoor adjustment for high dimensional treatments and confounders. We cast backdoor adjustment as an optimization problem in variational inference without reliance on proxy variables and hidden confounders. Empirically, our method is able to estimate interventional likelihood in a variety of high dimensional settings, including semi-synthetic X-ray medical data. To the best of our knowledge, this is the first application of backdoor adjustment in which all the relevant variables are high dimensional.
Multi-source domain adaptation (MSDA) methods aim to transfer knowledge from multiple labeled source domains to an unlabeled target domain. Although current methods achieve target joint distribution identifiability by enforcing minimal changes across domains, they often necessitate stringent conditions, such as an adequate number of domains, monotonic transformation of latent variables, and invariant label distributions. These requirements are challenging to satisfy in real-world applications. To mitigate the need for these strict assumptions, we propose a subspace identification theory that guarantees the disentanglement of domain-invariant and domain-specific variables under less restrictive constraints regarding domain numbers and transformation properties, thereby facilitating domain adaptation by minimizing the impact of domain shifts on invariant variables. Based on this theory, we develop a Subspace Identification Guarantee (SIG) model that leverages variational inference. Furthermore, the SIG model incorporates class-aware conditional alignment to accommodate target shifts where label distributions change with the domains. Experimental results demonstrate that our SIG model outperforms existing MSDA techniques on various benchmark datasets, highlighting its effectiveness in real-world applications.
Sampling a target probability distribution with an unknown normalization constant is a fundamental challenge in computational science and engineering. Recent work shows that algorithms derived by considering gradient flows in the space of probability measures open up new avenues for algorithm development. This paper makes three contributions to this sampling approach by scrutinizing the design components of such gradient flows. Any instantiation of a gradient flow for sampling needs an energy functional and a metric to determine the flow, as well as numerical approximations of the flow to derive algorithms. Our first contribution is to show that the Kullback-Leibler divergence, as an energy functional, has the unique property (among all f-divergences) that gradient flows resulting from it do not depend on the normalization constant of the target distribution. Our second contribution is to study the choice of metric from the perspective of invariance. The Fisher-Rao metric is known as the unique choice (up to scaling) that is diffeomorphism invariant. As a computationally tractable alternative, we introduce a relaxed, affine invariance property for the metrics and gradient flows. In particular, we construct various affine invariant Wasserstein and Stein gradient flows. Affine invariant gradient flows are shown to behave more favorably than their non-affine-invariant counterparts when sampling highly anisotropic distributions, in theory and by using particle methods. Our third contribution is to study, and develop efficient algorithms based on Gaussian approximations of the gradient flows; this leads to an alternative to particle methods. We establish connections between various Gaussian approximate gradient flows, discuss their relation to gradient methods arising from parametric variational inference, and study their convergence properties both theoretically and numerically.
The Bayesian estimation of GARCH-family models has been typically addressed through Monte Carlo sampling. Variational Inference is gaining popularity and attention as a robust approach for Bayesian inference in complex machine learning models; however, its adoption in econometrics and finance is limited. This paper discusses the extent to which Variational Inference constitutes a reliable and feasible alternative to Monte Carlo sampling for Bayesian inference in GARCH-like models. Through a large-scale experiment involving the constituents of the S&P 500 index, several Variational Inference optimizers, a variety of volatility models, and a case study, we show that Variational Inference is an attractive, remarkably well-calibrated, and competitive method for Bayesian learning.
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.