Contrastive Learning has recently received interest due to its success in self-supervised representation learning in the computer vision domain. However, the origins of Contrastive Learning date as far back as the 1990s and its development has spanned across many fields and domains including Metric Learning and natural language processing. In this paper we provide a comprehensive literature review and we propose a general Contrastive Representation Learning framework that simplifies and unifies many different contrastive learning methods. We also provide a taxonomy for each of the components of contrastive learning in order to summarise it and distinguish it from other forms of machine learning. We then discuss the inductive biases which are present in any contrastive learning system and we analyse our framework under different views from various sub-fields of Machine Learning. Examples of how contrastive learning has been applied in computer vision, natural language processing, audio processing, and others, as well as in Reinforcement Learning are also presented. Finally, we discuss the challenges and some of the most promising future research directions ahead.

Symmetric functions, which take as input an unordered, fixed-size set, are known to be universally representable by neural networks that enforce permutation invariance. These architectures only give guarantees for fixed input sizes, yet in many practical applications, including point clouds and particle physics, a relevant notion of generalization should include varying the input size. In this work we treat symmetric functions (of any size) as functions over probability measures, and study the learning and representation of neural networks defined on measures. By focusing on shallow architectures, we establish approximation and generalization bounds under different choices of regularization (such as RKHS and variation norms), that capture a hierarchy of functional spaces with increasing degree of non-linear learning. The resulting models can be learned efficiently and enjoy generalization guarantees that extend across input sizes, as we verify empirically.

Unlike in the traditional statistical modeling for which a user typically hand-specify a prior, Neural Processes (NPs) implicitly define a broad class of stochastic processes with neural networks. Given a data stream, NP learns a stochastic process that best describes the data. While this "data-driven" way of learning stochastic processes has proven to handle various types of data, NPs still rely on an assumption that uncertainty in stochastic processes is modeled by a single latent variable, which potentially limits the flexibility. To this end, we propose the Boostrapping Neural Process (BNP), a novel extension of the NP family using the bootstrap. The bootstrap is a classical data-driven technique for estimating uncertainty, which allows BNP to learn the stochasticity in NPs without assuming a particular form. We demonstrate the efficacy of BNP on various types of data and its robustness in the presence of model-data mismatch.

Convolutional Neural Networks (CNNs) have proven to be state-of-the-art models for supervised computer vision tasks, such as image classification. However, large labeled data sets are generally needed for the training and validation of such models. In many domains, unlabeled data is available but labeling is expensive, for instance when specific expert knowledge is required. Active Learning (AL) is one approach to mitigate the problem of limited labeled data. Through selecting the most informative and representative data instances for labeling, AL can contribute to more efficient learning of the model. Recent AL methods for CNNs propose different solutions for the selection of instances to be labeled. However, they do not perform consistently well and are often computationally expensive. In this paper, we propose a novel AL algorithm that efficiently learns from unlabeled data by capturing high prediction uncertainty. By replacing the softmax standard output of a CNN with the parameters of a Dirichlet density, the model learns to identify data instances that contribute efficiently to improving model performance during training. We demonstrate in several experiments with publicly available data that our method consistently outperforms other state-of-the-art AL approaches. It can be easily implemented and does not require extensive computational resources for training. Additionally, we are able to show the benefits of the approach on a real-world medical use case in the field of automated detection of visual signals for pneumonia on chest radiographs.

We propose a flexible framework for clustering hypergraph-structured data based on recently proposed random walks utilizing edge-dependent vertex weights. When incorporating edge-dependent vertex weights (EDVW), a weight is associated with each vertex-hyperedge pair, yielding a weighted incidence matrix of the hypergraph. Such weightings have been utilized in term-document representations of text data sets. We explain how random walks with EDVW serve to construct different hypergraph Laplacian matrices, and then develop a suite of clustering methods that use these incidence matrices and Laplacians for hypergraph clustering. Using several data sets from real-life applications, we compare the performance of these clustering algorithms experimentally against a variety of existing hypergraph clustering methods. We show that the proposed methods produce higher-quality clusters and conclude by highlighting avenues for future work.

We consider generalized linear models in regimes where the number of nonzero components of the signal and accessible data points are sublinear with respect to the size of the signal. We prove a variational formula for the asymptotic mutual information per sample when the system size grows to infinity. This result allows us to derive an expression for the minimum mean-square error (MMSE) of the Bayesian estimator when the signal entries have a discrete distribution with finite support. We find that, for such signals and suitable vanishing scalings of the sparsity and sampling rate, the MMSE is nonincreasing piecewise constant. In specific instances the MMSE even displays an all-or-nothing phase transition, that is, the MMSE sharply jumps from its maximum value to zero at a critical sampling rate. The all-or-nothing phenomenon has previously been shown to occur in high-dimensional linear regression. Our analysis goes beyond the linear case and applies to learning the weights of a perceptron with general activation function in a teacher-student scenario. In particular, we discuss an all-or-nothing phenomenon for the generalization error with a sublinear set of training examples.

Recent advances in image clustering typically focus on learning better deep representations. In contrast, we present an orthogonal approach that does not rely on abstract features but instead learns to predict image transformations and performs clustering directly in image space. This learning process naturally fits in the gradient-based training of K-means and Gaussian mixture model, without requiring any additional loss or hyper-parameters. It leads us to two new deep transformation-invariant clustering frameworks, which jointly learn prototypes and transformations. More specifically, we use deep learning modules that enable us to resolve invariance to spatial, color and morphological transformations. Our approach is conceptually simple and comes with several advantages, including the possibility to easily adapt the desired invariance to the task and a strong interpretability of both cluster centers and assignments to clusters. We demonstrate that our novel approach yields competitive and highly promising results on standard image clustering benchmarks. Finally, we showcase its robustness and the advantages of its improved interpretability by visualizing clustering results over real photograph collections.

Accurate quantification of uncertainty is crucial for real-world applications of machine learning. However, modern deep neural networks still produce unreliable predictive uncertainty, often yielding over-confident predictions. In this paper, we are concerned with getting well-calibrated predictions in regression tasks. We propose the calibrated regression method using the maximum mean discrepancy by minimizing the kernel embedding measure. Theoretically, the calibration error of our method asymptotically converges to zero when the sample size is large enough. Experiments on non-trivial real datasets show that our method can produce well-calibrated and sharp prediction intervals, which outperforms the related state-of-the-art methods.

We study the Stein Variational Gradient Descent (SVGD) algorithm, which optimises a set of particles to approximate a target probability distribution $\pi\propto e^{-V}$ on $\mathbb{R}^d$. In the population limit, SVGD performs gradient descent in the space of probability distributions on the KL divergence with respect to $\pi$, where the gradient is smoothed through a kernel integral operator. In this paper, we provide a novel finite time analysis for the SVGD algorithm. We provide a descent lemma establishing that the algorithm decreases the objective at each iteration, and rates of convergence. We also provide a convergence result of the finite particle system corresponding to the practical implementation of SVGD to its population version.

In the context of statistical supervised learning, the noiseless linear model assumes that there exists a deterministic linear relation $Y = \langle \theta_*, X \rangle$ between the random output $Y$ and the random feature vector $\Phi(U)$, a potentially non-linear transformation of the inputs $U$. We analyze the convergence of single-pass, fixed step-size stochastic gradient descent on the least-square risk under this model. The convergence of the iterates to the optimum $\theta_*$ and the decay of the generalization error follow polynomial convergence rates with exponents that both depend on the regularities of the optimum $\theta_*$ and of the feature vectors $\Phi(u)$. We interpret our result in the reproducing kernel Hilbert space framework. As a special case, we analyze an online algorithm for estimating a real function on the unit interval from the noiseless observation of its value at randomly sampled points; the convergence depends on the Sobolev smoothness of the function and of a chosen kernel. Finally, we apply our analysis beyond the supervised learning setting to obtain convergence rates for the averaging process (a.k.a. gossip algorithm) on a graph depending on its spectral dimension.