Learning the multivariate distribution of data is a core challenge in statistics and machine learning. Traditional methods aim for the probability density function (PDF) and are limited by the curse of dimensionality. Modern neural methods are mostly based on black-box models, lacking identifiability guarantees. In this work, we aim to learn multivariate cumulative distribution functions (CDFs), as they can handle mixed random variables, allow efficient'box' probability evaluation, and have the potential to overcome local sample scarcity owing to their cumulative nature. We show that any grid-sampled version of a joint CDF of mixed random variables admits a universal representation as a naive Bayes model via the Canonical Polyadic (tensor-rank) decomposition. By introducing a low-rank model, either directly in the raw data domain, or indirectly in a transformed (Copula) domain, the resulting model affords efficient sampling, closed form inference and uncertainty quantification, and comes with uniqueness guarantees under relatively mild conditions. We demonstrate the superior performance of the proposed model in several synthetic and real datasets and applications including regression, sampling and data imputation. Interestingly, our experiments with real data show that it is possible to obtain better density/mass estimates indirectly via a low-rank CDF model, than a low-rank PDF/PMF model.

Minimizing the inclusive Kullback-Leibler (KL) divergence with stochastic gradient descent (SGD) is challenging since its gradient is defined as an integral over the posterior. Recently, multiple methods have been proposed to run SGD with biased gradient estimates obtained from a Markov chain. This paper provides the first non-asymptotic convergence analysis of these methods by establishing their mixing rate and gradient variance. To do this, we demonstrate that these methods-which we collectively refer to as Markov chain score ascent (MCSA) methods-can be cast as special cases of the Markov chain gradient descent framework. Furthermore, by leveraging this new understanding, we develop a novel MCSA scheme, parallel MCSA (pMCSA), that achieves a tighter bound on the gradient variance. We demonstrate that this improved theoretical result translates to superior empirical performance.

We propose a general purpose Bayesian inference algorithm for expensive likelihoods, replacing the stochastic term in the Langevin equation with a deterministic density gradient term. The particle density is evaluated from the current particle positions using a Normalizing Flow (NF), which is differentiable and has good generalization properties in high dimensions. We take advantage of NF preconditioning and NF based Metropolis-Hastings updates for a faster convergence. We show on various examples that the method is competitive against state of the art sampling methods.

As a key natural language processing (NLP) task, word sense disambiguation (WSD) evaluates how well NLP models can understand the lexical semantics of words under specific contexts. Benefited from the large-scale annotation, current WSD systems have achieved impressive performances in English by combining supervised learning with lexical knowledge. However, such success is hard to be replicated in other languages, where we only have limited annotations.In this paper, based on the multilingual lexicon BabelNet describing the same set of concepts across languages, we propose building knowledge and supervised-based Multilingual Word Sense Disambiguation (MWSD) systems. We build unified sense representations for multiple languages and address the annotation scarcity problem for MWSD by transferring annotations from rich-sourced languages to poorer ones. With the unified sense representations, annotations from multiple languages can be jointly trained to benefit the MWSD tasks. Evaluations of SemEval-13 and SemEval-15 datasets demonstrate the effectiveness of our methodology.

Subgraph representation learning based on Graph Neural Network (GNN) has exhibited broad applications in scientific advancements, such as predictions of molecular structure-property relationships and collective cellular function. In particular, graph augmentation techniques have shown promising results in improving graph-based and node-based classification tasks. Still, they have rarely been explored in the existing GNN-based subgraph representation learning studies. In this study, we develop a novel multi-view augmentation mechanism to improve subgraph representation learning models and thus the accuracy of downstream prediction tasks. Our augmentation technique creates multiple variants of subgraphs and embeds these variants into the original graph to achieve highly improved training efficiency, scalability, and accuracy. Benchmark experiments on several real-world biological and physiological datasets demonstrate the superiority of our proposed multi-view augmentation techniques in subgraph representation learning.

The scattering transform is a multilayered, wavelet-based transform initially introduced as a model of convolutional neural networks (CNNs) that has played a foundational role in our understanding of these networks' stability and invariance properties. Subsequently, there has been widespread interest in extending the success of CNNs to data sets with non-Euclidean structure, such as graphs and manifolds, leading to the emerging field of geometric deep learning. In order to improve our understanding of the architectures used in this new field, several papers have proposed generalizations of the scattering transform for non-Euclidean data structures such as undirected graphs and compact Riemannian manifolds without boundary. In this paper, we introduce a general, unified model for geometric scattering on measure spaces. Our proposed framework includes previous work on geometric scattering as special cases but also applies to more general settings such as directed graphs, signed graphs, and manifolds with boundary. We propose a new criterion that identifies to which groups a useful representation should be invariant and show that this criterion is sufficient to guarantee that the scattering transform has desirable stability and invariance properties. Additionally, we consider finite measure spaces that are obtained from randomly sampling an unknown manifold. We propose two methods for constructing a data-driven graph on which the associated graph scattering transform approximates the scattering transform on the underlying manifold. Moreover, we use a diffusion-maps based approach to prove quantitative estimates on the rate of convergence of one of these approximations as the number of sample points tends to infinity. Lastly, we showcase the utility of our method on spherical images, directed graphs, and on high-dimensional single-cell data.

Modern quantum annealers can find high-quality solutions to combinatorial optimisation objectives given as quadratic unconstrained binary optimisation (QUBO) problems. Unfortunately, obtaining suitable QUBO forms in computer vision remains challenging and currently requires problem-specific analytical derivations. Moreover, such explicit formulations impose tangible constraints on solution encodings. In stark contrast to prior work, this paper proposes to learn QUBO forms from data through gradient backpropagation instead of deriving them. As a result, the solution encodings can be chosen flexibly and compactly. Furthermore, our methodology is general and virtually independent of the specifics of the target problem type. We demonstrate the advantages of learnt QUBOs on the diverse problem types of graph matching, 2D point cloud alignment and 3D rotation estimation. Our results are competitive with the previous quantum state of the art while requiring much fewer logical and physical qubits, enabling our method to scale to larger problems. The code and the new dataset will be open-sourced.

In many modern applications of deep neural networks, where the amount of labeled examples for training is limited, distillation with unlabeled examples [8, 20] has been enormously successful. In this two-stage training paradigm a larger and more sophisticated "teacher model" -- typically non-deployable for the purposes of the application -- is trained to learn from the limited amount of available training data in the first stage. In the second stage, the teacher model is used to generate labels on an unlabeled dataset, which is usually much larger in size than the original dataset the teacher itself was trained on. These labels are then utilized to train the "student model", namely the model which will actually be deployed. Notably, distillation with unlabeled examples is the most commonly used training-paradigm in applications where one finetunes and distills from very large-scale foundational models such as BERT [13] and GPT-3 [5] and, additionally, it can be used to significantly improve distillation on supervised examples only (see e.g.

Nowadays, the development of information technology is growing rapidly. In the big data era, the privacy of personal information has been more pronounced. The major challenge is to find a way to guarantee that sensitive personal information is not disclosed while data is published and analyzed. Centralized differential privacy is established on the assumption of a trusted third-party data curator. However, this assumption is not always true in reality. As a new privacy preservation model, local differential privacy has relatively strong privacy guarantees. Although federated learning has relatively been a privacy-preserving approach for distributed learning, it still introduces various privacy concerns. To avoid privacy threats and reduce communication costs, in this article, we propose integrating federated learning and local differential privacy with momentum gradient descent to improve the performance of machine learning models.

Recent years have witnessed the effectiveness of contrastive learning in obtaining the representation of dataset that is useful in interpretation and downstream tasks. However, the mechanism that describes this effectiveness have not been thoroughly analyzed, and many studies have been conducted to investigate the data structures captured by contrastive learning. In particular, the recent study of \citet{content_isolate} has shown that contrastive learning is capable of decomposing the data space into the space that is invariant to all augmentations and its complement. In this paper, we introduce the notion of invariance-adapted latent space that decomposes the data space into the intersections of the invariant spaces of each augmentation and their complements. This decomposition generalizes the one introduced in \citet{content_isolate}, and describes a structure that is analogous to the frequencies in the harmonic analysis of a group. We experimentally show that contrastive learning with lasso-type metric can be used to find an invariance-adapted latent space, thereby suggesting a new potential for the contrastive learning. We also investigate when such a latent space can be identified up to mixings within each component.