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Estimating and optimizing Mutual Information (MI) is core to many problems in machine learning; however, bounding MI in high dimensions is challenging. To establish tractable and scalable objectives, recent work has turned to variational…

There are two main approaches to the distributed representation of words: low-dimensional deep learning embeddings and high-dimensional distributional models, in which each dimension corresponds to a context word. In this paper, we combine…

Statistical query (SQ) algorithms are algorithms that have access to an {\em SQ oracle} for the input distribution $D$ instead of i.i.d.~ samples from $D$. Given a query function $\phi:X \rightarrow [-1,1]$, the oracle returns an estimate…

Efficiently learning mixture of Gaussians is a fundamental problem in statistics and learning theory. Given samples coming from a random one out of k Gaussian distributions in Rn, the learning problem asks to estimate the means and the…

Machine learning and quantum computing are two technologies each with the potential for altering how computation is performed to address previously untenable problems. Kernel methods for machine learning are ubiquitous for pattern…

Convolutional Neural Network (CNN) is a popular model in computer vision and has the advantage of making good use of the correlation information of data. However, CNN is challenging to learn efficiently if the given dimension of data or…

Sample complexity bounds are a common performance metric in the Reinforcement Learning literature. In the discounted cost, infinite horizon setting, all of the known bounds have a factor that is a polynomial in $1/(1-\gamma)$, where $\gamma…

Estimation of the large $Q$-matrix in Cognitive Diagnosis Models (CDMs) with many items and latent attributes from observational data has been a huge challenge due to its high computational cost. Borrowing ideas from deep learning…

Quantum entanglement is a key resource in quantum computing and quantum information processing tasks. However, its quantification remains a major challenge since it cannot be directly extracted from physical observables. To address this…

Contrastive learning has emerged as a powerful paradigm for self-supervised representation learning. This work analyzes the theoretical limits of contrastive learning under nasty noise, where an adversary modifies or replaces training…

We propose and analyze a kernelized version of Q-learning. Although a kernel space is typically infinite-dimensional, extensive study has shown that generalization is only affected by the effective dimension of the data. We incorporate such…

In Statistical Learning, the Vapnik-Chervonenkis (VC) dimension is an important combinatorial property of classifiers. To our knowledge, no theoretical results yet exist for the VC dimension of edited nearest-neighbour (1NN) classifiers…

Continual learning, or lifelong learning, is a formidable current challenge to machine learning. It requires the learner to solve a sequence of $k$ different learning tasks, one after the other, while retaining its aptitude for earlier…

Deep neural networks have established themselves as one of the most promising machine learning techniques. Training such models at large scales is often parallelized, giving rise to the concept of distributed deep learning. Distributed…

Recent progress in diverse intelligence has shown simple learning capacities below the organism level - single cells and even molecular networks. However, there are still many knowledge gaps around learning capacity above the organism…

Neural Combinatorial Optimization attempts to learn good heuristics for solving a set of problems using Neural Network models and Reinforcement Learning. Recently, its good performance has encouraged many practitioners to develop neural…

Understanding self-supervised learning is important but challenging. Previous theoretical works study the role of pretraining losses, and view neural networks as general black boxes. However, the recent work of Saunshi et al. argues that…

This paper surveys quantum learning theory: the theoretical aspects of machine learning using quantum computers. We describe the main results known for three models of learning: exact learning from membership queries, and Probably…

Machine learning techniques are used to predict theoretical constraints such as unitarity and boundedness from below in extensions of the Standard Model. This approach has proven effective for models incorporating additional SU(2) scalar…

Understanding minimal assumptions that enable learning and generalization is perhaps the central question of learning theory. Several celebrated results in statistical learning theory, such as the VC theorem and Littlestone's…