Since their inception, Variational Autoencoders (VAEs) have become central in machine learning. Despite their widespread use, numerous questions regarding their theoretical properties remain open. Using PAC-Bayesian theory, this work develops statistical guarantees for VAEs. First, we derive the first PAC-Bayesian bound for posterior distributions conditioned on individual samples from the data-generating distribution. Then, we utilize this result to develop generalization guarantees for the VAE's reconstruction loss, as well as upper bounds on the distance between the input and the regenerated distributions. More importantly, we provide upper bounds on the Wasserstein distance between the input distribution and the distribution defined by the VAE's generative model.

Graph Neural Networks (GNN) have recently gained popularity in the forecasting domain due to their ability to model complex spatial and temporal patterns in tasks such as traffic forecasting and region-based demand forecasting. Most of these methods require a predefined graph as input, whereas in real-life multivariate time series problems, a well-predefined dependency graph rarely exists. This requirement makes it harder for GNNs to be utilised widely for multivariate forecasting problems in other domains such as retail or energy. In this paper, we propose a hybrid approach combining neural networks and statistical structure learning models to self-learn the dependencies and construct a dynamically changing dependency graph from multivariate data aiming to enable the use of GNNs for multivariate forecasting even when a well-defined graph does not exist. The statistical structure modeling in conjunction with neural networks provides a well-principled and efficient approach by bringing in causal semantics to determine dependencies among the series. Finally, we demonstrate significantly improved performance using our proposed approach on real-world benchmark datasets without a pre-defined dependency graph.

Machine learning models are often trained to predict the outcome resulting from a human decision. For example, if a doctor decides to test a patient for disease, will the patient test positive? A challenge is that the human decision censors the outcome data: we only observe test outcomes for patients doctors historically tested. Untested patients, for whom outcomes are unobserved, may differ from tested patients along observed and unobserved dimensions. We propose a Bayesian model class which captures this setting. The purpose of the model is to accurately estimate risk for both tested and untested patients. Estimating this model is challenging due to the wide range of possibilities for untested patients. To address this, we propose two domain constraints which are plausible in health settings: a prevalence constraint, where the overall disease prevalence is known, and an expertise constraint, where the human decision-maker deviates from purely risk-based decision-making only along a constrained feature set. We show theoretically and on synthetic data that domain constraints improve parameter inference. We apply our model to a case study of cancer risk prediction, showing that the model's inferred risk predicts cancer diagnoses, its inferred testing policy captures known public health policies, and it can identify suboptimalities in test allocation. Though our case study is in healthcare, our analysis reveals a general class of domain constraints which can improve model estimation in many settings.

Recently, artificial intelligence for drug discovery has raised increasing interest in both machine learning and chemistry domains. The fundamental building block for drug discovery is molecule geometry and thus, the molecule's geometrical representation is the main bottleneck to better utilize machine learning techniques for drug discovery. In this work, we propose a pretraining method for molecule joint auto-encoding (MoleculeJAE). MoleculeJAE can learn both the 2D bond (topology) and 3D conformation (geometry) information, and a diffusion process model is applied to mimic the augmented trajectories of such two modalities, based on which, MoleculeJAE will learn the inherent chemical structure in a self-supervised manner. Thus, the pretrained geometrical representation in MoleculeJAE is expected to benefit downstream geometry-related tasks. Empirically, MoleculeJAE proves its effectiveness by reaching state-of-the-art performance on 15 out of 20 tasks by comparing it with 12 competitive baselines.

Imitation learning methods seek to learn from an expert either through behavioral cloning (BC) of the policy or inverse reinforcement learning (IRL) of the reward. Such methods enable agents to learn complex tasks from humans that are difficult to capture with hand-designed reward functions. Choosing BC or IRL for imitation depends on the quality and state-action coverage of the demonstrations, as well as additional access to the Markov decision process. Hybrid strategies that combine BC and IRL are not common, as initial policy optimization against inaccurate rewards diminishes the benefit of pretraining the policy with BC. This work derives an imitation method that captures the strengths of both BC and IRL. In the entropy-regularized ('soft') reinforcement learning setting, we show that the behaviour-cloned policy can be used as both a shaped reward and a critic hypothesis space by inverting the regularized policy update. This coherency facilitates fine-tuning cloned policies using the reward estimate and additional interactions with the environment. This approach conveniently achieves imitation learning through initial behaviour cloning, followed by refinement via RL with online or offline data sources. The simplicity of the approach enables graceful scaling to high-dimensional and vision-based tasks, with stable learning and minimal hyperparameter tuning, in contrast to adversarial approaches. For the open-source implementation and simulation results, see https://joemwatson.github.io/csil/.

Social media networks have become a significant aspect of people's lives, serving as a platform for their ideas, opinions and emotions. Consequently, automated sentiment analysis (SA) is critical for recognising people's feelings in ways that other information sources cannot. The analysis of these feelings revealed various applications, including brand evaluations, YouTube film reviews and healthcare applications. As social media continues to develop, people post a massive amount of information in different forms, including text, photos, audio and video. Thus, traditional SA algorithms have become limited, as they do not consider the expressiveness of other modalities. By including such characteristics from various material sources, these multimodal data streams provide new opportunities for optimising the expected results beyond text-based SA. Our study focuses on the forefront field of multimodal SA, which examines visual and textual data posted on social media networks. Many people are more likely to utilise this information to express themselves on these platforms. To serve as a resource for academics in this rapidly growing field, we introduce a comprehensive overview of textual and visual SA, including data pre-processing, feature extraction techniques, sentiment benchmark datasets, and the efficacy of multiple classification methodologies suited to each field. We also provide a brief introduction of the most frequently utilised data fusion strategies and a summary of existing research on visual-textual SA. Finally, we highlight the most significant challenges and investigate several important sentiment applications.

Gaussian noise was then added to produce a noisy simulated data. Given the data, the posterior of a model (a pixelated image of the undistorted background source) could be calculated by adding the likelihood and the prior terms. Furthermore since the model is perfectly linear (and known) and the noise and the prior are Gaussian, the posterior is a high-dimensional Gaussian posterior that could be calculated analytically, allowing us to compare the samples drawn with GGNS with the analytic solution. Figure 2 shows a comparison between the true image, and its noise, and the one recovered by GGNS. We see that we can recover both the correct image, and the noise distribution. We emphasize that this is a uni-modal problem and that the experiment's goal is to demonstrate the capability of GGNS to sample in high dimensions (in this case, 256), such as images, and to test the agreement between the samples and a baseline analytic solution.

Estimating the parameters of ordinary differential equations (ODEs) is of fundamental importance in many scientific applications. While ODEs are typically approximated with deterministic algorithms, new research on probabilistic solvers indicates that they produce more reliable parameter estimates by better accounting for numerical errors. However, many ODE systems are highly sensitive to their parameter values. This produces deep local maxima in the likelihood function -- a problem which existing probabilistic solvers have yet to resolve. Here we present a novel probabilistic ODE likelihood approximation, DALTON, which can dramatically reduce parameter sensitivity by learning from noisy ODE measurements in a data-adaptive manner. Our approximation scales linearly in both ODE variables and time discretization points, and is applicable to ODEs with both partially-unobserved components and non-Gaussian measurement models. Several examples demonstrate that DALTON produces more accurate parameter estimates via numerical optimization than existing probabilistic ODE solvers, and even in some cases than the exact ODE likelihood itself.

We propose a solution for linear inverse problems based on higher-order Langevin diffusion. More precisely, we propose pre-conditioned second-order and third-order Langevin dynamics that provably sample from the posterior distribution of our unknown variables of interest while being computationally more efficient than their first-order counterpart and the non-conditioned versions of both dynamics. Moreover, we prove that both pre-conditioned dynamics are well-defined and have the same unique invariant distributions as the non-conditioned cases. We also incorporate an annealing procedure that has the double benefit of further accelerating the convergence of the algorithm and allowing us to accommodate the case where the unknown variables are discrete. Numerical experiments in two different tasks in communications (MIMO symbol detection and channel estimation) and in three tasks for images showcase the generality of our method and illustrate the high performance achieved relative to competing approaches (including learning-based ones) while having comparable or lower computational complexity.

The heteroscedastic probabilistic principal component analysis (PCA) technique, a variant of the classic PCA that considers data heterogeneity, is receiving more and more attention in the data science and signal processing communities. In this paper, to estimate the underlying low-dimensional linear subspace (simply called \emph{ground truth}) from available heterogeneous data samples, we consider the associated non-convex maximum-likelihood estimation problem, which involves maximizing a sum of heterogeneous quadratic forms over an orthogonality constraint (HQPOC). We propose a first-order method -- generalized power method (GPM) -- to tackle the problem and establish its \emph{estimation performance} guarantee. Specifically, we show that, given a suitable initialization, the distances between the iterates generated by GPM and the ground truth decrease at least geometrically to some threshold associated with the residual part of certain "population-residual decomposition". In establishing the estimation performance result, we prove a novel local error bound property of another closely related optimization problem, namely quadratic optimization with orthogonality constraint (QPOC), which is new and can be of independent interest. Numerical experiments are conducted to demonstrate the superior performance of GPM in both Gaussian noise and sub-Gaussian noise settings.