arXiv research

Polynomial-time test for detecting dense subgraphs in heterogeneous networks.

Polynomial delay algorithm tests causal models with hidden variables.

The paper provides an almost optimal learning and testing algorithm for sparse polynomials.

Paper proves first non-trivial PTF testing lower bounds for NGCA.

This work finds a point with small test error in polynomial time for mildly overparameterized neural nets.

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

A new algorithm reduces CI tests for causal graph recovery.

New methods test discrete distributions faster with local privacy constraints.

We study the atomic embeddability testing problem, which is a common generalization of clustered planarity (c-planarity, for short) and thickenability testing, and present a polynomial-time algorithm for this problem, thereby giving the first polynomial-time algorithm for c-planarity. C-planarity was introduced in 1995…

A new family of conformal test martingales based on Legendre polynomials for online exchangeability testing.

Detecting correlated trees helps align sparse graphs.

Study phase transitions in identifying infected individuals using group testing.

It has recently been shown that the problem of testing global convexity of polynomials of degree four is {strongly} NP-hard, answering an open question of N.Z. Shor. This result is minimal in the degree of the polynomial when global convexity is of concern. In a number of applications however, one is interested in test…

The paper explores how low-degree polynomials can detect shuffled linear regression models.

Improving scalability and stability of Stein discrepancies for scalable goodness-of-fit testing

MixCIT tests conditional independence for mixed data types efficiently and reliably.

A new method tests Expected Shortfall by analyzing both duration and severity of VaR violations.

Statistical query algorithms and low-degree tests are nearly equivalent in high-dimensional hypothesis testing.

PDSim simulates and estimates commodity futures prices using polynomial diffusion models.

We propose a new, precise integrality conjecture for the colored Kauffman polynomial of knots and links inspired by large N dualities and the structure of topological string theory on orientifolds. According to this conjecture, the natural knot invariant in an unoriented theory involves both the colored Kauffman polyno…

The colored HOMFLY polynomial is the quantum invariant of oriented links in $S^3$ associated with irreducible representations of the quantum group $U_q(\mathrm{sl}_N)$. In this paper, using an approach to calculate quantum invariants of links via cabling-projection rule, we derive a formula for the colored HOMFLY polyn…

Researchers compute and predict knot volumes using colored Jones polynomials.

A new method for assessing Bayesian sampling quality, PSD, is proposed and shown to be more powerful and efficient.

We prove near-tight concentration of measure for polynomial functions of the Ising model under high temperature. For any degree $d$, we show that a degree-$d$ polynomial of a $n$-spin Ising model exhibits exponential tails that scale as $\exp(-r^{2/d})$ at radius $r=\tildeΩ_d(n^{d/2})$. Our concentration radius is opti…

We classify the Montesinos links up to mutation and 5-move equivalence, and obtain from this a Jones and Kauffman polynomial test for a Montesinos link.

New method uses almost orthonormal bases to prove low-degree lower bounds in complex statistical models.

Tests for classifier independence without ground truth labels.

New findings on Jones polynomial for 4-strand braids.

Like all other knot polynomials, the superpolynomials should be defined in arbitrary representation R of the gauge group in (refined) Chern-Simons theory. However, not a single example is yet known of a superpolynomial beyond symmetric or antisymmetric representations. We consider the expansion of the superpolynomial a…

The paper explores statistical limits for detecting correlation in tree structures.

Study shows a tradeoff between sample complexity and computational efficiency for learning halfspaces with random noise.

Survey on using low-degree polynomials to assess statistical tasks complexity.

A new method optimizes MMD test power by dynamically selecting kernels, overcoming traditional trade-offs.

Recent years have demonstrated that using random feature maps can significantly decrease the training and testing times of kernel-based algorithms without significantly lowering their accuracy. Regrettably, because random features are target-agnostic, typically thousands of such features are necessary to achieve accept…

A mathematical framework connects neural networks and polynomial regression for better model understanding.

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…

Invariant polynomials improve machine learning performance.

The vanishing ideal is a set of polynomials that takes zero value on the given data points. Originally proposed in computer algebra, the vanishing ideal has been recently exploited for extracting the nonlinear structures of data in many applications. To avoid overfitting to noisy data, the polynomials are often designe…

We analyze kernel matrices in polynomial high-dimensional settings and explain double descent in KRR.

Volterra and polynomial regression models play a major role in nonlinear system identification and inference tasks. Exciting applications ranging from neuroscience to genome-wide association analysis build on these models with the additional requirement of parsimony. This requirement has high interpretative value, but …

We study the design of computationally efficient algorithms with provable guarantees, that are robust to adversarial (test time) perturbations. While there has been an proliferation of recent work on this topic due to its connections to test time robustness of deep networks, there is limited theoretical understanding o…

This paper is about two related decision theoretic problems, nonparametric two-sample testing and independence testing. There is a belief that two recently proposed solutions, based on kernels and distances between pairs of points, behave well in high-dimensional settings. We identify different sources of misconception…

Develops AMITE for analyzing neural network nonlinearities.

We connect two important conjectures in the theory of knot polynomials. The first one is the property Al_R(q) = Al_{[1]}(q^{|R|}) for all single hook Young diagrams R, which is known to hold for all knots. The second conjecture claims that all the mixing matrices U_{i} in the relation {\cal R}_i = U_i{\cal R}_1U_i^{-1}…

We perform a finite sample analysis of the detection levels for sparse principal components of a high-dimensional covariance matrix. Our minimax optimal test is based on a sparse eigenvalue statistic. Alas, computing this test is known to be NP-complete in general, and we describe a computationally efficient alternativ…

Model inference for dynamical systems aims to estimate the future behaviour of a system from observations. Purely model-free statistical methods, such as Artificial Neural Networks, tend to perform poorly for such tasks. They are therefore not well suited to many questions from applications, for example in Bayesian fil…

Optimal AFs minimize RFR test error and sensitivity.

Numerical experiments support conjecture about opers and nonabelian Hodge.