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We revisit Gerber's Informational Quality (IQ) framework, a data-driven approach for constructing correlation matrices from co-movement evidence, and address two obstacles that limit its use in portfolio optimization: guaranteeing positive…
Most self-supervised learning (SSL) methods learn continuous visual representations by aligning different views of the same input, offering limited control over how information is structured across representation dimensions. In this work,…
We introduce a technique for estimating a structured covariance matrix from observations of a random vector which have been sketched. Each observed random vector $\boldsymbol{x}_t$ is reduced to a single number by taking its inner product…
Deep neural networks employ specialized architectures for vision, sequential and language tasks, yet this proliferation obscures their underlying commonalities. We introduce a unified matrix-order framework that casts convolutional,…
We study how group symmetry helps improve data efficiency and generalization for end-to-end differentiable planning algorithms when symmetry appears in decision-making tasks. Motivated by equivariant convolution networks, we treat the path…
Most algorithms for solving optimization problems or finding saddle points of convex-concave functions are fixed-point algorithms. In this work we consider the generic problem of finding a fixed point of an average of operators, or an…
We adapt multilevel, force-directed graph layout techniques to visualizing dynamic graphs in which vertices and edges are added and removed in an online fashion (i.e., unpredictably). We maintain multiple levels of coarseness using a…
Random projections or sketching are widely used in many algorithmic and learning contexts. Here we study the performance of iterative Hessian sketch for least-squares problems. By leveraging and extending recent results from random matrix…
The efficient solution of large-scale multiterm linear matrix equations is a challenging task in numerical linear algebra, and it is a largely open problem. We propose a new iterative scheme for symmetric and positive definite operators,…
Natural videos provide rich visual contents for self-supervised learning. Yet most existing approaches for learning spatio-temporal representations rely on manually trimmed videos, leading to limited diversity in visual patterns and limited…
Convolutional neural networks have been shown to develop internal representations, which correspond closely to semantically meaningful objects and parts, although trained solely on class labels. Class Activation Mapping (CAM) is a recent…
The paper presents a strategy to construct an incremental Singular Value Decomposition (SVD) for time-evolving, spatially 3D discrete data sets. A low memory access procedure for reducing and deploying the snapshot data is presented.…
Scalable algorithms to solve optimization and regression tasks even approximately, are needed to work with large datasets. In this paper we study efficient techniques from matrix sketching to solve a variety of convex constrained regression…
Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to…
We consider classification tasks in the regime of scarce labeled training data in high dimensional feature space, where specific expert knowledge is also available. We propose a new hybrid optimization algorithm that solves the elastic-net…
A robot's ability to act is fundamentally constrained by what it can perceive. Many existing approaches to visual representation learning utilize general-purpose training criteria, e.g. image reconstruction, smoothness in latent space, or…
Eigenvalue transformations appear ubiquitously in scientific computation, ranging from matrix polynomials to differential equations, and are beyond the reach of the quantum singular value transformation framework. In this work, we study the…
This paper describes Sparse Frequent Directions, a variant of Frequent Directions for sketching sparse matrices. It resembles the original algorithm in many ways: both receive the rows of an input matrix $A^{n \times d}$ one by one in the…
The core of cross-modal matching is to accurately measure the similarity between different modalities in a unified representation space. However, compared to textual descriptions of a certain perspective, the visual modality has more…
The cone of positive-semidefinite (PSD) matrices is fundamental in convex optimization, and we extend this notion to tensors, defining PSD tensors, which correspond to separable quantum states. We study the convex optimization problem over…