Cross-modal Retrieval methods build similarity relations between vision and language modalities by jointly learning a common representation space. However, the predictions are often unreliable due to the Aleatoric uncertainty, which is induced by low-quality data, e.g., corrupt images, fast-paced videos, and non-detailed texts. In this paper, we propose a novel Prototype-based Aleatoric Uncertainty Quantification (PAU) framework to provide trustworthy predictions by quantifying the uncertainty arisen from the inherent data ambiguity. Concretely, we first construct a set of various learnable prototypes for each modality to represent the entire semantics subspace. Then Dempster-Shafer Theory and Subjective Logic Theory are utilized to build an evidential theoretical framework by associating evidence with Dirichlet Distribution parameters.

Training of the neural autoregressive density estimator (NADE) can be viewed as doing one step of probabilistic inference on missing values in data. We propose a new model that extends this inference scheme to multiple steps, arguing that it is easier to learn to improve a reconstruction in k steps rather than to learn to reconstruct in a single inference step. The proposed model is an unsupervised building block for deep learning that combines the desirable properties of NADE and multi-predictive training: (1) Its test likelihood can be computed analytically, (2) it is easy to generate independent samples from it, and (3) it uses an inference engine that is a superset of variational inference for Boltzmann machines. The proposed NADE-k is competitive with the state-of-the-art in density estimation on the two datasets tested.

The goal of sequential event prediction is to estimate the next event based on a sequence of historical events, with applications to sequential recommendation, user behavior analysis and clinical treatment. In practice, the next-event prediction models are trained with sequential data collected at one time and need to generalize to newly arrived sequences in remote future, which requires models to handle temporal distribution shift from training to testing. In this paper, we first take a data-generating perspective to reveal a negative result that existing approaches with maximum likelihood estimation would fail for distribution shift due to the latent context confounder, i.e., the common cause for the historical events and the next event. Then we devise a new learning objective based on backdoor adjustment and further harness variational inference to make it tractable for sequence learning problems. On top of that, we propose a framework with hierarchical branching structures for learning context-specific representations.

We develop a model by choosing the maximum entropy distribution from the set of models satisfying certain smoothness and independence criteria; we show that inference on this model generalizes local kernel estimation to the context of Bayesian inference on stochastic processes. Our model enables Bayesian inference in contexts when standard techniques like Gaussian process inference are too expensive to apply. Exact inference on our model is possible for any likelihood function from the exponential family. Inference is then highly efficient, requiring only O(log N) time and O(N) space at run time. We demonstrate our algorithm on several problems and show quantifiable improvement in both speed and performance relative to models based on the Gaussian process.

Neural signals are typical nonstationary data where the functional mapping between neural activities and the intentions (such as the velocity of movements) can occasionally change. Existing studies mostly use a fixed neural decoder, thus suffering from an unstable performance given neural functional changes. We propose a novel evolutionary ensemble framework (EvoEnsemble) to dynamically cope with changes in neural signals by evolving the decoder model accordingly. EvoEnsemble integrates evolutionary computation algorithms in a Bayesian framework where the fitness of models can be sequentially computed with their likelihoods according to the incoming data at each time slot, which enables online tracking of time-varying functions. Two strategies of evolve-at-changes and history-model-archive are designed to further improve efficiency and stability.

Since their initial introduction, score-based diffusion models (SDMs) have been successfully applied to solve a variety of linear inverse problems in finite-dimensional vector spaces due to their ability to efficiently approximate the posterior distribution. However, using SDMs for inverse problems in infinite-dimensional function spaces has only been addressed recently, primarily through methods that learn the unconditional score. While this approach is advantageous for some inverse problems, it is mostly heuristic and involves numerous computationally costly forward operator evaluations during posterior sampling. To address these limitations, we propose a theoretically grounded method for sampling from the posterior of infinite-dimensional Bayesian linear inverse problems based on amortized conditional SDMs. In particular, we prove that one of the most successful approaches for estimating the conditional score in finite dimensions--the conditional denoising estimator--can also be applied in infinite dimensions.

Distributed learning of probabilistic models from multiple data repositories with minimum communication is increasingly important. We study a simple communication-efficient learning framework that first calculates the local maximum likelihood estimates (MLE) based on the data subsets, and then combines the local MLEs to achieve the best possible approximation to the global MLE, based on the whole dataset jointly. We study the statistical properties of this framework, showing that the loss of efficiency compared to the global setting relates to how much the underlying distribution families deviate from full exponential families, drawing connection to the theory of information loss by Fisher, Rao and Efron. We show that the full-exponential-family-ness" represents the lower bound of the error rate of arbitrary combinations of local MLEs, and is achieved by a KL-divergence-based combination method but not by a more common linear combination method. We also study the empirical properties of the KL and linear combination methods, showing that the KL method significantly outperforms linear combination in practical settings with issues such as model misspecification, non-convexity, and heterogeneous data partitions."

Diffusion Probabilistic Models (DPMs) have shown a powerful capacity of generating high-quality image samples. Recently, diffusion autoencoders (Diff-AE) have been proposed to explore DPMs for representation learning via autoencoding. Their key idea is to jointly train an encoder for discovering meaningful representations from images and a conditional DPM as the decoder for reconstructing images. Specifically, we find that the reason that pre-trained DPMs fail to reconstruct an image from its latent variables is due to the information loss of forward process, which causes a gap between their predicted posterior mean and the true one. From this perspective, the classifier-guided sampling method can be explained as computing an extra mean shift to fill the gap, reconstructing the lost class information in samples.

Let p be an unknown and arbitrary probability distribution over [0,1) . We consider the problem of \emph{density estimation}, in which a learning algorithm is given i.i.d. The main contribution of this paper is a highly efficient density estimation algorithm for learning using a variable-width histogram, i.e., a hypothesis distribution with a piecewise constant probability density function. In more detail, for any k and \eps, we give an algorithm that makes \tilde{O}(k/\eps 2) draws from p, runs in \tilde{O}(k/\eps 2) time, and outputs a hypothesis distribution h that is piecewise constant with O(k \log 2(1/\eps)) pieces. With high probability the hypothesis h satisfies \dtv(p,h) \leq C \cdot \opt_k(p) \eps, where \dtv denotes the total variation distance (statistical distance), C is a universal constant, and \opt_k(p) is the smallest total variation distance between p and any k -piecewise constant distribution.

However, training and sampling from EBMs continue to pose significant challenges. The widely-used Denoising Score Matching (DSM) method for scalable EBM training suffers from inconsistency issues, causing the energy model to learn a noisy data distribution. In this work, we propose an efficient sampling framework: (pseudo)-Gibbs sampling with moment matching, which enables effective sampling from the underlying clean model when given a noisy model that has been well-trained via DSM. We explore the benefits of our approach compared to related methods and demonstrate how to scale the method to high-dimensional datasets.