Bayesian deep learning and conformal prediction are two methods that have been used to convey uncertainty and increase safety in machine learning systems. We focus on combining Bayesian deep learning with split conformal prediction and how this combination effects out-of-distribution coverage; particularly in the case of multiclass image classification. We suggest that if the model is generally underconfident on the calibration set, then the resultant conformal sets may exhibit worse out-of-distribution coverage compared to simple predictive credible sets. Conversely, if the model is overconfident on the calibration set, the use of conformal prediction may improve out-of-distribution coverage. We evaluate prediction sets as a result of combining split conformal methods and neural networks trained with (i) stochastic gradient descent, (ii) deep ensembles, and (iii) mean-field variational inference. Our results suggest that combining Bayesian deep learning models with split conformal prediction can, in some cases, cause unintended consequences such as reducing out-of-distribution coverage.
We present elliptical processes, a family of non-parametric probabilistic models that subsume Gaussian processes and Student's t processes. This generalization includes a range of new heavy-tailed behaviors while retaining computational tractability. Elliptical processes are based on a representation of elliptical distributions as a continuous mixture of Gaussian distributions. We parameterize this mixture distribution as a spline normalizing flow, which we train using variational inference. The proposed form of the variational posterior enables a sparse variational elliptical process applicable to large-scale problems. We highlight advantages compared to Gaussian processes through regression and classification experiments. Elliptical processes can supersede Gaussian processes in several settings, including cases where the likelihood is non-Gaussian or when accurate tail modeling is essential.
Large language models (LLM)-based speech synthesis has been widely adopted in zero-shot speech synthesis. However, they require a large-scale data and possess the same limitations as previous autoregressive speech models, including slow inference speed and lack of robustness. This paper proposes HierSpeech++, a fast and strong zero-shot speech synthesizer for text-to-speech (TTS) and voice conversion (VC). We verified that hierarchical speech synthesis frameworks could significantly improve the robustness and expressiveness of the synthetic speech. Furthermore, we significantly improve the naturalness and speaker similarity of synthetic speech even in zero-shot speech synthesis scenarios. For text-to-speech, we adopt the text-to-vec framework, which generates a self-supervised speech representation and an F0 representation based on text representations and prosody prompts. Then, HierSpeech++ generates speech from the generated vector, F0, and voice prompt. We further introduce a high-efficient speech super-resolution framework from 16 kHz to 48 kHz. The experimental results demonstrated that the hierarchical variational autoencoder could be a strong zero-shot speech synthesizer given that it outperforms LLM-based and diffusion-based models. Moreover, we achieved the first human-level quality zero-shot speech synthesis. Audio samples and source code are available at https://github.com/sh-lee-prml/HierSpeechpp.
In deep learning, Bayesian neural networks (BNN) provide the role of robustness analysis, and the minimax method is used to be a conservative choice in the traditional Bayesian field. In this paper, we study a conservative BNN with the minimax method and formulate a two-player game between a deterministic neural network $f$ and a sampling stochastic neural network $f + r*\xi$. From this perspective, we understand the closed-loop neural networks with the minimax loss and reveal their connection to the BNN. We test the models on simple data sets, study their robustness under noise perturbation, and report some issues for searching $r$.
The customization of recommended content to users holds significant importance in enhancing user experiences across a wide spectrum of applications such as e-commerce, music, and shopping. Graph-based methods have achieved considerable performance by capturing user-item interactions. However, these methods tend to utilize randomly constructed embeddings in the dataset used for training the recommender, which lacks any user preferences. Here, we propose the concept of variational embeddings as a means of pre-training the recommender system to improve the feature propagation through the layers of graph convolutional networks (GCNs). The graph variational embedding collaborative filtering (GVECF) is introduced as a novel framework to incorporate representations learned through a variational graph auto-encoder which are embedded into a GCN-based collaborative filtering. This approach effectively transforms latent high-order user-item interactions into more trainable vectors, ultimately resulting in better performance in terms of recall and normalized discounted cumulative gain(NDCG) metrics. The experiments conducted on benchmark datasets demonstrate that our proposed method achieves up to 13.78% improvement in the recall over the test data.
Sepsis is a life-threatening condition triggered by an extreme infection response. Our objective is to forecast sepsis patient outcomes using their medical history and treatments, while learning interpretable state representations to assess patients' risks in developing various adverse outcomes. While neural networks excel in outcome prediction, their limited interpretability remains a key issue. In this work, we use knowledge distillation via constrained variational inference to distill the knowledge of a powerful "teacher" neural network model with high predictive power to train a "student" latent variable model to learn interpretable hidden state representations to achieve high predictive performance for sepsis outcome prediction. Using real-world data from the MIMIC-IV database, we trained an LSTM as the "teacher" model to predict mortality for sepsis patients, given information about their recent history of vital signs, lab values and treatments. For our student model, we use an autoregressive hidden Markov model (AR-HMM) to learn interpretable hidden states from patients' clinical time series, and use the posterior distribution of the learned state representations to predict various downstream outcomes, including hospital mortality, pulmonary edema, need for diuretics, dialysis, and mechanical ventilation. Our results show that our approach successfully incorporates the constraint to achieve high predictive power similar to the teacher model, while maintaining the generative performance.
We study mean-field variational inference in a Bayesian linear model when the sample size n is comparable to the dimension p. In high dimensions, the common approach of minimizing a Kullback-Leibler divergence from the posterior distribution, or maximizing an evidence lower bound, may deviate from the true posterior mean and underestimate posterior uncertainty. We study instead minimization of the TAP free energy, showing in a high-dimensional asymptotic framework that it has a local minimizer which provides a consistent estimate of the posterior marginals and may be used for correctly calibrated posterior inference. Geometrically, we show that the landscape of the TAP free energy is strongly convex in an extensive neighborhood of this local minimizer, which under certain general conditions can be found by an Approximate Message Passing (AMP) algorithm. We then exhibit an efficient algorithm that linearly converges to the minimizer within this local neighborhood. In settings where it is conjectured that no efficient algorithm can find this local neighborhood, we prove analogous geometric properties for a local minimizer of the TAP free energy reachable by AMP, and show that posterior inference based on this minimizer remains correctly calibrated.
In this work, we present a novel machine learning approach for pricing high-dimensional American options based on the modified Gaussian process regression (GPR). We incorporate deep kernel learning and sparse variational Gaussian processes to address the challenges traditionally associated with GPR. These challenges include its diminished reliability in high-dimensional scenarios and the excessive computational costs associated with processing extensive numbers of simulated paths Our findings indicate that the proposed method surpasses the performance of the least squares Monte Carlo method in high-dimensional scenarios, particularly when the underlying assets are modeled by Merton's jump diffusion model. Moreover, our approach does not exhibit a significant increase in computational time as the number of dimensions grows. Consequently, this method emerges as a potential tool for alleviating the challenges posed by the curse of dimensionality.
This paper studies the problem of modeling multi-agent dynamical systems, where agents could interact mutually to influence their behaviors. Recent research predominantly uses geometric graphs to depict these mutual interactions, which are then captured by powerful graph neural networks (GNNs). However, predicting interacting dynamics in challenging scenarios such as out-of-distribution shift and complicated underlying rules remains unsolved. In this paper, we propose a new approach named Prototypical Graph ODE (PGODE) to address the problem. The core of PGODE is to incorporate prototype decomposition from contextual knowledge into a continuous graph ODE framework. Specifically, PGODE employs representation disentanglement and system parameters to extract both object-level and system-level contexts from historical trajectories, which allows us to explicitly model their independent influence and thus enhances the generalization capability under system changes. Then, we integrate these disentangled latent representations into a graph ODE model, which determines a combination of various interacting prototypes for enhanced model expressivity. The entire model is optimized using an end-to-end variational inference framework to maximize the likelihood. Extensive experiments in both in-distribution and out-of-distribution settings validate the superiority of PGODE compared to various baselines.
The recently proposed tensor robust principal component analysis (TRPCA) methods based on tensor singular value decomposition (t-SVD) have achieved numerous successes in many fields. However, most of these methods are only applicable to third-order tensors, whereas the data obtained in practice are often of higher order, such as fourth-order color videos, fourth-order hyperspectral videos, and fifth-order light-field images. Additionally, in the t-SVD framework, the multi-rank of a tensor can describe more fine-grained low-rank structure in the tensor compared with the tubal rank. However, determining the multi-rank of a tensor is a much more difficult problem than determining the tubal rank. Moreover, most of the existing TRPCA methods do not explicitly model the noises except the sparse noise, which may compromise the accuracy of estimating the low-rank tensor. In this work, we propose a novel high-order TRPCA method, named as Low-Multi-rank High-order Bayesian Robust Tensor Factorization (LMH-BRTF), within the Bayesian framework. Specifically, we decompose the observed corrupted tensor into three parts, i.e., the low-rank component, the sparse component, and the noise component. By constructing a low-rank model for the low-rank component based on the order-$d$ t-SVD and introducing a proper prior for the model, LMH-BRTF can automatically determine the tensor multi-rank. Meanwhile, benefiting from the explicit modeling of both the sparse and noise components, the proposed method can leverage information from the noises more effectivly, leading to an improved performance of TRPCA. Then, an efficient variational inference algorithm is established for parameters estimation. Empirical studies on synthetic and real-world datasets demonstrate the effectiveness of the proposed method in terms of both qualitative and quantitative results.
Maximizing the log-likelihood is a crucial aspect of learning latent variable models, and variational inference (VI) stands as the commonly adopted method. However, VI can encounter challenges in achieving a high log-likelihood when dealing with complicated posterior distributions. In response to this limitation, we introduce a novel variational importance sampling (VIS) approach that directly estimates and maximizes the log-likelihood. VIS leverages the optimal proposal distribution, achieved by minimizing the forward $\chi^2$ divergence, to enhance log-likelihood estimation. We apply VIS to various popular latent variable models, including mixture models, variational auto-encoders, and partially observable generalized linear models. Results demonstrate that our approach consistently outperforms state-of-the-art baselines, both in terms of log-likelihood and model parameter estimation.
With the increased use of data-driven approaches and machine learning-based methods in material science, the importance of reliable uncertainty quantification (UQ) of the predicted variables for informed decision-making cannot be overstated. UQ in material property prediction poses unique challenges, including the multi-scale and multi-physics nature of advanced materials, intricate interactions between numerous factors, limited availability of large curated datasets for model training, etc. Recently, Bayesian Neural Networks (BNNs) have emerged as a promising approach for UQ, offering a probabilistic framework for capturing uncertainties within neural networks. In this work, we introduce an approach for UQ within physics-informed BNNs, which integrates knowledge from governing laws in material modeling to guide the models toward physically consistent predictions. To evaluate the effectiveness of this approach, we present case studies for predicting the creep rupture life of steel alloys. Experimental validation with three datasets of collected measurements from creep tests demonstrates the ability of BNNs to produce accurate point and uncertainty estimates that are competitive or exceed the performance of the conventional method of Gaussian Process Regression. Similarly, we evaluated the suitability of BNNs for UQ in an active learning application and reported competitive performance. The most promising framework for creep life prediction is BNNs based on Markov Chain Monte Carlo approximation of the posterior distribution of network parameters, as it provided more reliable results in comparison to BNNs based on variational inference approximation or related NNs with probabilistic outputs. The codes are available at: https://github.com/avakanski/Creep-uncertainty-quantification.
Randomized controlled trials (RCTs) are the accepted standard for treatment effect estimation but they can be infeasible due to ethical reasons and prohibitive costs. Single-arm trials, where all patients belong to the treatment group, can be a viable alternative but require access to an external control group. We propose an identifiable deep latent-variable model for this scenario that can also account for missing covariate observations by modeling their structured missingness patterns. Our method uses amortized variational inference to learn both group-specific and identifiable shared latent representations, which can subsequently be used for {\em (i)} patient matching if treatment outcomes are not available for the treatment group, or for {\em (ii)} direct treatment effect estimation assuming outcomes are available for both groups. We evaluate the model on a public benchmark as well as on a data set consisting of a published RCT study and real-world electronic health records. Compared to previous methods, our results show improved performance both for direct treatment effect estimation as well as for effect estimation via patient matching.
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.
Encoding only the task-related information from the raw data, \ie, disentangled representation learning, can greatly contribute to the robustness and generalizability of models. Although significant advances have been made by regularizing the information in representations with information theory, two major challenges remain: 1) the representation compression inevitably leads to performance drop; 2) the disentanglement constraints on representations are in complicated optimization. To these issues, we introduce Bayesian networks with transmitted information to formulate the interaction among input and representations during disentanglement. Building upon this framework, we propose \textbf{DisTIB} (\textbf{T}ransmitted \textbf{I}nformation \textbf{B}ottleneck for \textbf{Dis}entangled representation learning), a novel objective that navigates the balance between information compression and preservation. We employ variational inference to derive a tractable estimation for DisTIB. This estimation can be simply optimized via standard gradient descent with a reparameterization trick. Moreover, we theoretically prove that DisTIB can achieve optimal disentanglement, underscoring its superior efficacy. To solidify our claims, we conduct extensive experiments on various downstream tasks to demonstrate the appealing efficacy of DisTIB and validate our theoretical analyses.
Class imbalance in graph data presents significant challenges for node classification. While existing methods, such as SMOTE-based approaches, partially mitigate this issue, they still exhibit limitations in constructing imbalanced graphs. Generative self-supervised learning (SSL) methods, exemplified by graph autoencoders (GAEs), offer a promising solution by directly generating minority nodes from the data itself, yet their potential remains underexplored. In this paper, we delve into the shortcomings of SMOTE-based approaches in the construction of imbalanced graphs. Furthermore, we introduce VIGraph, a simple yet effective generative SSL approach that relies on the Variational GAE as the fundamental model. VIGraph strictly adheres to the concept of imbalance when constructing imbalanced graphs and innovatively leverages the variational inference (VI) ability of Variational GAE to generate nodes for minority classes. VIGraph introduces comprehensive training strategies, including cross-view contrastive learning at the decoding phase to capture semantic knowledge, adjacency matrix reconstruction to preserve graph structure, and alignment strategy to ensure stable training. VIGraph can generate high-quality nodes directly usable for classification, eliminating the need to integrate the generated nodes back to the graph as well as additional retraining found in SMOTE-based methods. We conduct extensive experiments, results from which demonstrate the superiority and generality of our approach.
We propose Diffusion Model Variational Inference (DMVI), a novel method for automated approximate inference in probabilistic programming languages (PPLs). DMVI utilizes diffusion models as variational approximations to the true posterior distribution by deriving a novel bound to the marginal likelihood objective used in Bayesian modelling. DMVI is easy to implement, allows hassle-free inference in PPLs without the drawbacks of, e.g., variational inference using normalizing flows, and does not make any constraints on the underlying neural network model. We evaluate DMVI on a set of common Bayesian models and show that its posterior inferences are in general more accurate than those of contemporary methods used in PPLs while having a similar computational cost and requiring less manual tuning.
We introduce Support Decomposition Variational Inference (SDVI), a new variational inference (VI) approach for probabilistic programs with stochastic support. Existing approaches to this problem rely on designing a single global variational guide on a variable-by-variable basis, while maintaining the stochastic control flow of the original program. SDVI instead breaks the program down into sub-programs with static support, before automatically building separate sub-guides for each. This decomposition significantly aids in the construction of suitable variational families, enabling, in turn, substantial improvements in inference performance.
Variational inference is a technique that approximates a target distribution by optimizing within the parameter space of variational families. On the other hand, Wasserstein gradient flows describe optimization within the space of probability measures where they do not necessarily admit a parametric density function. In this paper, we bridge the gap between these two methods. We demonstrate that, under certain conditions, the Bures-Wasserstein gradient flow can be recast as the Euclidean gradient flow where its forward Euler scheme is the standard black-box variational inference algorithm. Specifically, the vector field of the gradient flow is generated via the path-derivative gradient estimator. We also offer an alternative perspective on the path-derivative gradient, framing it as a distillation procedure to the Wasserstein gradient flow. Distillations can be extended to encompass $f$-divergences and non-Gaussian variational families. This extension yields a new gradient estimator for $f$-divergences, readily implementable using contemporary machine learning libraries like PyTorch or TensorFlow.
In this paper, we introduce ProNet, an novel deep learning approach designed for multi-horizon time series forecasting, adaptively blending autoregressive (AR) and non-autoregressive (NAR) strategies. Our method involves dividing the forecasting horizon into segments, predicting the most crucial steps in each segment non-autoregressively, and the remaining steps autoregressively. The segmentation process relies on latent variables, which effectively capture the significance of individual time steps through variational inference. In comparison to AR models, ProNet showcases remarkable advantages, requiring fewer AR iterations, resulting in faster prediction speed, and mitigating error accumulation. On the other hand, when compared to NAR models, ProNet takes into account the interdependency of predictions in the output space, leading to improved forecasting accuracy. Our comprehensive evaluation, encompassing four large datasets, and an ablation study, demonstrate the effectiveness of ProNet, highlighting its superior performance in terms of accuracy and prediction speed, outperforming state-of-the-art AR and NAR forecasting models.