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Incorporating sparsity priors in learning tasks can give rise to simple, and interpretable models for complex high dimensional data. Sparse models have found widespread use in structure discovery, recovering data from corruptions, and a…

Our world is full of asymmetries. Gravity and wind can make reaching a place easier than coming back. Social artifacts such as genealogy charts and citation graphs are inherently directed. In reinforcement learning and control, optimal…

Quantum computers are growing in size, and design decisions are being made now that attempt to squeeze more computation out of these machines. In this spirit, we design a method to boost the computational power of near-term quantum…

In this paper we present a novel non-parametric method of simplifying piecewise linear curves and we apply this method as a statistical approximation of structure within sequential data in the plane. We consider the problem of minimizing…

We introduce a quantum algorithm that produces approximate solutions for combinatorial optimization problems. The algorithm depends on a positive integer p and the quality of the approximation improves as p is increased. The quantum circuit…

We provide a new quantum algorithm that efficiently determines the quality of a least-squares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently (Harrow et al., Phys.…

In this paper, we consider high-dimensional Lp-quantile regression which only requires a low order moment of the error and is also a natural generalization of the above methods and Lp-regression as well. The loss function of Lp-quantile…

We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…

We introduce a new convex optimization problem, termed quadratic decomposable submodular function minimization. The problem is closely related to decomposable submodular function minimization and arises in many learning on graphs and…

Machine learning methods have nowadays become easy-to-use tools for constructing high-dimensional interatomic potentials with ab initio accuracy. Although machine learned interatomic potentials are generally orders of magnitude faster than…

Many practical optimization problems lack strong convexity. Fortunately, recent studies have revealed that first-order algorithms also enjoy linear convergences under various weaker regularity conditions. While the relationship among…

Max-cut, clustering, and many other partitioning problems that are of significant importance to machine learning and other scientific fields are NP-hard, a reality that has motivated researchers to develop a wealth of approximation…

Quantum computation, a completely different paradigm of computing, benefits from theoretically proven speed-ups for certain problems and opens up the possibility of exactly studying the properties of quantum systems. Yet, because of the…

Bayesian optimization relies on iteratively constructing and optimizing an acquisition function. The latter turns out to be a challenging, non-convex optimization problem itself. Despite the relative importance of this step, most algorithms…

Model-based derivative-free optimization (DFO) methods are an important class of DFO methods that are known to struggle with solving high-dimensional optimization problems. Recent research has shown that incorporating random subspaces into…

We propose a prediction procedure for the functional linear quantile regression model by using partial quantile covariance techniques and develop a simple partial quantile regression (SIMPQR) algorithm to efficiently extract partial…

Classification is a common task in machine learning. Random features (RFs) stand as a central technique for scalable learning algorithms based on kernel methods, and more recently proposed optimized random features, sampled depending on the…

We propose an inexact variable-metric proximal point algorithm to accelerate gradient-based optimization algorithms. The proposed scheme, called QNing can be notably applied to incremental first-order methods such as the stochastic…

Approximate computing techniques have been successful in reducing computation and power costs in several domains. However, error sensitive applications in high-performance computing are unable to benefit from existing approximate computing…

Linear regression is a widely used technique to fit linear models and finds widespread applications across different areas such as machine learning and statistics. In most real-world scenarios, however, linear regression problems are often…