arXiv research

Spaces of polynomials are shown to be Euclidean balls.

Study geometric structures and their interactions under different metrics.

nn2poly converts neural networks into interpretable polynomial models.

Speech-driven facial animation involves using a speech signal to generate realistic videos of talking faces. Recent deep learning approaches to facial synthesis rely on extracting low-dimensional representations and concatenating them, followed by a decoding step of the concatenated vector. This accounts for only first…

New methods test discrete distributions faster with local privacy constraints.

We consider learning under the constraint of local differential privacy (LDP). For many learning problems known efficient algorithms in this model require many rounds of communication between the server and the clients holding the data points. Yet multi-round protocols are prohibitively slow in practice due to network …

Paper addresses ERM in LDP, reducing sample complexity for smooth and convex losses.

Reformulated sigma models for complex Grassmannians using Gross-Neveu formalism.

We study the problem of approximate ranking from observations of pairwise interactions. The goal is to estimate the underlying ranks of $n$ objects from data through interactions of comparison or collaboration. Under a general framework of approximate ranking models, we characterize the exact optimal statistical error …

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…

Proposes a graph dynamics prior for more accurate relational inference.

Unified model for interactive estimation with improved learnability measure.

New algorithm learns sparse linear MDPs with polynomial interactions, improving sample complexity.

xDeepInt learns both vector-wise and bit-wise feature interactions.

ProxySHAP approximates Shapley and Banzhaf interactions efficiently.

Polynomial networks and factorization machines are two recently-proposed models that can efficiently use feature interactions in classification and regression tasks. In this paper, we revisit both models from a unified perspective. Based on this new view, we study the properties of both models and propose new efficient…

New method learns near-optimal policies with polynomial samples in A and H.

The paper analyzes tensor recovery from symmetric rank-one measurements using information theory.

Classifies flat knots up to 8 crossings using Lyndon words.

This is an extended version of a talk given at the conference "Algebra and Topology in Interaction" on the occasion of the 70th Anniversary of D.B. Fuchs at UC Davis in September 2009. It is a brief survey of an area originated around 1995 by I. Gelfand and the author.

New algorithm tames non-linear growth in stochastic optimization.

A method for interpreting SVMs using polynomial kernels, revealing model complexity.

Unified framework for lower bounds in interactive decision making.

Can we effectively learn a nonlinear representation in time comparable to linear learning? We describe a new algorithm that explicitly and adaptively expands higher-order interaction features over base linear representations. The algorithm is designed for extreme computational efficiency, and an extensive experimental …

Bayesian adaptive PCE method improves surrogate modeling and sensitivity analysis.

In this paper, we study the Empirical Risk Minimization problem in the non-interactive local model of differential privacy. In the case of constant or low dimensionality ($p\ll n$), we first show that if the ERM loss function is $(\infty, T)$-smooth, then we can avoid a dependence of the sample complexity, to achieve e…

Polylab is a MATLAB toolbox for multivariate polynomial modeling.

Paper tackles efficient HMM learning with conditional samples.

The extragradient method accelerates convergence in complex game dynamics.

This paper analyzes in details the Batalin-Vilkovisky quantization procedure for BF theories on n-dimensional manifolds and describes a suitable superformalism to deal with the master equation and the search of observables. In particular, generalized Wilson loops for BF theories with additional polynomial B-interaction…

Proposes ICE-based metric for better understanding interactions in black-box models.

New robust algorithms improve learning with feature feedback.

Kernel discriminant analysis uses nonlinear embeddings to improve classification.

DCIts interprets complex time series data with interpretable coefficients.

We use Floer's exact triangle to study the u-map (cup product with the 4-dimensional class) in the Floer cohomology groups of admissible SO(3) bundles over closed, oriented 3-manifolds. In the case of non-trivial bundles we show that (u^2-64)^n = 0 for some positive integer n. For homology 3-spheres Y the same holds fo…

Computer simulation has become the standard tool in many engineering fields for designing and optimizing systems, as well as for assessing their reliability. To cope with demanding analysis such as optimization and reliability, surrogate models (a.k.a meta-models) have been increasingly investigated in the last decade.…

A fast algorithm speeds up training of pairwise kernels.

In this paper, we study the problem of structure learning for Bayesian networks in which nodes take discrete values. The problem is NP-hard in general but we show that under certain conditions we can recover the true structure of a Bayesian network with sufficient number of samples. We develop a mathematical model whic…

The paper establishes a nearly-sharp statistical threshold for efficient learning in Latent MDPs with separated components.

Modern graph or network datasets often contain rich structure that goes beyond simple pairwise connections between nodes. This calls for complex representations that can capture, for instance, edges of different types as well as so-called "higher-order interactions" that involve more than two nodes at a time. However, …

Study improves ERM for heavy-tailed data with dependent inputs.

ParamBoost uses gradient boosting to create interpretable non-linear models with constraints.

New model handles complex non-linear relationships with hidden graph structures.

Solves challenges in estimating parameters of softmax gating Gaussian mixture models.

Unified analysis of MPLE for Ising models with bounded operator norm or infinity norm.

Negative momentum accelerates convergence in minimax games but at a suboptimal rate.

Improved RL algorithm stabilizes unknown linear systems with polynomial regret.

The paper tackles robust policy learning in multitask contextual bandits with adversarial users.