Related papers: Approximating the Number of Relevant Variables in …
We consider the problem of computing a $k$-sparse approximation to the Fourier transform of a length $N$ signal. Our main result is a randomized algorithm for computing such an approximation (i.e. achieving the $\ell_2/\ell_2$ sparse…
We consider approximating analytic functions on the interval $[-1,1]$ from their values at a set of $m+1$ equispaced nodes. A result of Platte, Trefethen \& Kuijlaars states that fast and stable approximation from equispaced samples is…
We give a quasipolynomial time algorithm for the graph matching problem (also known as noisy or robust graph isomorphism) on correlated random graphs. Specifically, for every $\gamma>0$, we give a $n^{O(\log n)}$ time algorithm that given a…
The problem of explaining the behavior of deep neural networks has recently gained a lot of attention. While several attribution methods have been proposed, most come without strong theoretical foundations, which raises questions about…
We study the fair k-set selection problem where we aim to select $k$ sets from a given set system such that the (weighted) occurrence times that each element appears in these $k$ selected sets are balanced, i.e., the maximum (weighted)…
Given a graph $G=(V, E)$ and and a proper labeling $f$ from $V$ to $\{1, ..., n\}$, we define $B(f)$ as the maximum absolute difference between $f(u)$ and $f(v)$ where $(u,v)\in E$. The bandwidth of $G$ is the minimum $B(f)$ for all $f$.…
Many inference problems in structured prediction can be modeled as maximizing a score function on a space of labels, where graphs are a natural representation to decompose the total score into a sum of unary (nodes) and pairwise (edges)…
In reinforcement learning, temporal difference (TD) is the most direct algorithm to learn the value function of a policy. For large or infinite state spaces, exact representations of the value function are usually not available, and it must…
We study the problem of supervised learning a metric space under discriminative constraints. Given a universe $X$ and sets ${\cal S}, {\cal D}\subset {X \choose 2}$ of similar and dissimilar pairs, we seek to find a mapping $f:X\to Y$, into…
Optimization problems are ubiquitous in our societies and are present in almost every segment of the economy. Most of these optimization problems are NP-hard and computationally demanding, often requiring approximate solutions for…
Fair classification and fair representation learning are two important problems in supervised and unsupervised fair machine learning, respectively. Fair classification asks for a classifier that maximizes accuracy on a given data…
In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…
Given the importance of floating-point~(FP) performance in numerous domains, several new variants of FP and its alternatives have been proposed (e.g., Bfloat16, TensorFloat32, and Posits). These representations do not have correctly rounded…
We define and study the complexity of robust polynomials for Boolean functions and the related fault-tolerant quantum decision trees, where input bits are perturbed by noise. We compare several different possible definitions. Our main…
We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it,…
Robust covariance estimation is the following, well-studied problem in high dimensional statistics: given $N$ samples from a $d$-dimensional Gaussian $\mathcal{N}(\boldsymbol{0}, \Sigma)$, but where an $\varepsilon$-fraction of the samples…
We study parity features as representations that can be evaluated entirely classically once the binary or quantized input representation and parity words are fixed, particularly when labels depend on higher-order feature interactions or…
We develop fast and memory efficient numerical methods for learning functions of many variables that admit sparse representations in terms of general bounded orthonormal tensor product bases. Such functions appear in many applications…
We consider the problem of testing whether an unknown low-degree polynomial $p$ over $\mathbb{R}^n$ is sparse versus far from sparse, given access to noisy evaluations of the polynomial $p$ at \emph{randomly chosen points}. This is a…
We study the problem of approximating the value of the matching polynomial on graphs with edge parameter $\gamma$, where $\gamma$ takes arbitrary values in the complex plane. When $\gamma$ is a positive real, Jerrum and Sinclair showed that…