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Data-driven modeling plays an increasingly important role in different areas of engineering. For most of existing methods, such as genetic programming (GP), the convergence speed might be too slow for large scale problems with a large…
Topology optimization has emerged as a popular approach to refine a component's design and increase its performance. However, current state-of-the-art topology optimization frameworks are compute-intensive, mainly due to multiple finite…
We study the problem of covering a given set of $n$ points in a high, $d$-dimensional space by the minimum enclosing polytope of a given arbitrary shape. We present algorithms that work for a large family of shapes, provided either only…
Near isometric orthogonal embeddings to lower dimensions are a fundamental tool in data science and machine learning. In this paper, we present the construction of such embeddings that minimizes the maximum distortion for a given set of…
Sampling edges from a graph in sublinear time is a fundamental problem and a powerful subroutine for designing sublinear-time algorithms. Suppose we have access to the vertices of the graph and know a constant-factor approximation to the…
In this paper we consider algorithm unfolding for the Multiple Measurement Vector (MMV) problem in the case where only few training samples are available. Algorithm unfolding has been shown to empirically speed-up in a data-driven way the…
We study the sample complexity of the best-case Empirical Risk Minimizer in the setting of stochastic convex optimization. We show that there exists an instance in which the sample size is linear in the dimension, learning is possible, but…
Machine Learning models incorporating multiple layered learning networks have been seen to provide effective models for various classification problems. The resulting optimization problem to solve for the optimal vector minimizing the…
The completion of a Euclidean distance matrix (EDM) from sparse and noisy observations is a fundamental challenge in signal processing, with applications in sensor network localization, acoustic room reconstruction, molecular conformation,…
In this paper, we consider the problem of minimizing a difference-of-convex objective over a nonlinear conic constraint, where the cone is closed, convex, pointed and has a nonempty interior. We assume that the support function of a compact…
Many metric learning tasks, such as triplet learning, nearest neighbor retrieval, and visualization, are treated primarily as embedding tasks where the ultimate metric is some variant of the Euclidean distance (e.g., cosine or Mahalanobis),…
The objective of ordinal embedding is to find a Euclidean representation of a set of abstract items, using only answers to triplet comparisons of the form "Is item $i$ closer to the item $j$ or item $k$?". In recent years, numerous…
Many estimation problems in robotics, computer vision, and learning require estimating unknown quantities in the face of outliers. Outliers are typically the result of incorrect data association or feature matching, and it is common to have…
Parallel machine scheduling has been extensively studied in the past decades, with applications ranging from production planning to job processing in large computing clusters. In this work we study some of these fundamental optimization…
Quadratic programming is a ubiquitous prototype in convex programming. Many machine learning problems can be formulated as quadratic programming, including the famous Support Vector Machines (SVMs). Linear and kernel SVMs have been among…
Linear dynamical systems are canonical models for learning-based control of plants with uncertain dynamics. The setting consists of a stochastic differential equation that captures the state evolution of the plant understudy, while the true…
Metric learning aims to learn a highly discriminative model encouraging the embeddings of similar classes to be close in the chosen metrics and pushed apart for dissimilar ones. The common recipe is to use an encoder to extract embeddings…
Efficiently computing accurate representations of high-dimensional data is essential for data analysis and unsupervised learning. Dendrograms, also known as ultrametrics, are widely used representations that preserve hierarchical…
Optimization problems aim to find the optimal solution, which is becoming increasingly complex and difficult to solve. Traditional evolutionary optimization methods always overlook the granular characteristics of solution space. In the real…
Much of the field of Machine Learning exhibits a prominent set of failure modes, including vulnerability to adversarial examples, poor out-of-distribution (OoD) detection, miscalibration, and willingness to memorize random labelings of…