arXiv research

New formula refutes random CSPs with fewer constraints.

Study disproves conjecture about low-degree polynomials in hypothesis testing.

Study learning and refutation in non-interactive LDP, showing sample complexity equivalence.

Paper refutes conjecture on tensor power iteration convergence in overcomplete models.

Proposes bounds on bias from low-dimensional representations in CATE estimation.

The problem of high-dimensional path-dependent optimal stopping (OS) is important to multiple academic communities and applications. Modern OS tasks often have a large number of decision epochs, and complicated non-Markovian dynamics, making them especially challenging. Standard approaches, often relying on ADP, dualit…

We study dual volume sampling, a method for selecting k columns from an n x m short and wide matrix (n <= k <= m) such that the probability of selection is proportional to the volume spanned by the rows of the induced submatrix. This method was proposed by Avron and Boutsidis (2013), who showed it to be a promising met…

We discuss the mathematician George Bruce Halsted's accusations against Carl Friedrich Gauss, as well as refutations both by the latter's American grandson Robert Gauss in a letter to Felix Klein, and by the historian of mathematics Florian Cajori.

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 their reliability. On the other hand, the literature on cooperative game theory sugg…

Learning the directed acyclic graph (DAG) structure of a Bayesian network from observational data is a notoriously difficult problem for which many hardness results are known. In this paper we propose a provably polynomial-time algorithm for learning sparse Gaussian Bayesian networks with equal noise variance --- a cla…

Gathering the most information by picking the least amount of data is a common task in experimental design or when exploring an unknown environment in reinforcement learning and robotics. A widely used measure for quantifying the information contained in some distribution of interest is its entropy. Greedily minimizing…

New algorithm achieves online calibration in polynomial time for high-dimensional problems.

For the tensor PCA (principal component analysis) problem, we propose a new hierarchy of increasingly powerful algorithms with increasing runtime. Our hierarchy is analogous to the sum-of-squares (SOS) hierarchy but is instead inspired by statistical physics and related algorithms such as belief propagation and AMP (ap…

We develop an algorithm of polynomial time complexity to construct the Grushko decomposition of fundamental groups of graphs of free groups with cyclic edge groups. Our methods rely on analysing vertex links of certain CAT(0) square complexes naturally associated with a special class of the above groups. Our main resul…

The paper challenges the notion that asset return doesn't affect Black-Scholes-Merton model.

Dictionary learning is a popular approach for inferring a hidden basis or dictionary in which data has a sparse representation. Data generated from the dictionary A (an n by m matrix, with m > n in the over-complete setting) is given by Y = AX where X is a matrix whose columns have supports chosen from a distribution o…

Note refutes examples of Landsberg surfaces with vanishing flag curvature.

In the noisy tensor completion problem we observe $m$ entries (whose location is chosen uniformly at random) from an unknown $n_1 \times n_2 \times n_3$ tensor $T$. We assume that $T$ is entry-wise close to being rank $r$. Our goal is to fill in its missing entries using as few observations as possible. Let $n = \max(n…

Example shows learnable distributions not privately learnable.

A new knot invariant is fast, strong, topologically meaningful, and fun.

Audit shows risk claims from distributional reinforcement learning agents are often false.

Polynomial-time method solves complex combinatorial semi-bandits.

Polynomial time algorithm matches correlated Gaussian matrices without vanishing correlation.

Path regularization reveals convex optimization in deep ReLU networks.

SAM minimizes loss sharpness, improving adversarial transferability.

Polynomial-time methods count and sample DAGs from equivalence classes.

We present the strongest known knot invariant that can be computed effectively (in polynomial time).

Investigates polynomial time algorithms for computing Khovanov homology of braids.

Polynomial-time private algorithm for robust estimation of mean and covariance in the presence of outliers.

Two new algorithms speed up TreeSHAP computation for tree-based models.

Making learners robust to adversarial perturbation at test time (i.e., evasion attacks) or training time (i.e., poisoning attacks) has emerged as a challenging task. It is known that for some natural settings, sublinear perturbations in the training phase or the testing phase can drastically decrease the quality of the…

This paper establishes for the first time the predictive performance of speed priors and their computational complexity. A speed prior is essentially a probability distribution that puts low probability on strings that are not efficiently computable. We propose a variant to the original speed prior (Schmidhuber, 2002),…

New polynomial-time solutions found for training ReLU networks, mirroring Max-Cut complexity.

Polynomial-time methods count and sample DAGs from Markov classes.

Coresets are efficient representations of data sets such that models trained on the coreset are provably competitive with models trained on the original data set. As such, they have been successfully used to scale up clustering models such as K-Means and Gaussian mixture models to massive data sets. However, until now,…

Polynomial-time algorithm matches correlated random graphs with non-vanishing correlation.

The generalization of Frobenius' theorem to foliations with singularities is usually attributed to Stefan and Sussmann, for their simultaneous discovery around 1973. However, their result is often referred to without caring much on the precise statement, as some sort of magic spell. This may be explained by the fact th…

We describe a polynomial-time algorithm to compute a (tight) geodesic between two curves in the curve graph. As well as enabling us to compute the distance between a pair of curves, this has several applications to mapping classes. For example, we can use these geodesics to compute the asymptotic translation length, Ni…

In this paper, we develop a new approach to learning high-dimensional Poisson directed acyclic graphical (DAG) models from only observational data without strong assumptions such as faithfulness and strong sparsity. A key component of our method is to decouple the ordering estimation or parent search where the problems…

Polynomial-time algorithm for near-optimal community detection in graphs.

In this paper we study the adaptive learnability of decision trees of depth at most $d$ from membership queries. This has many applications in automated scientific discovery such as drugs development and software update problem. Feldman solves the problem in a randomized polynomial time algorithm that asks $\tilde O(2^…

Polynomial-time algorithm learns causal graphs without parametric assumptions.

Algorithm classifies surface homeomorphisms with polynomial time complexity.

The paper proves a conjecture about spacetimes and singularities.

New algorithm recovers sparse measures in polynomial time.

New findings on community recovery in SBM with many communities.

Polynomial-time DP algorithm for learning Gaussians with matching sample complexity.

Polynomial-time algorithm learns ReLU networks without assumptions.