arXiv research

Study recovers tree structure in noisy MRFs with support size 3 or more.

New result on tensor recovery without strong assumptions.

We analyze the information-theoretic limits for the recovery of node labels in several network models. This includes the Stochastic Block Model, the Exponential Random Graph Model, the Latent Space Model, the Directed Preferential Attachment Model, and the Directed Small-world Model. For the Stochastic Block Model, the…

Detecting and recovering labels in binomial logistic mixtures is challenging due to an information gap.

New algorithms recover clusters with minimal queries, connecting margins to recoverability.

Neural interaction discoveries can be real or artifacts of model flexibility.

Unified framework for imitation learning via moment matching.

We discuss a variant of Thompson sampling for nonparametric reinforcement learning in a countable classes of general stochastic environments. These environments can be non-Markov, non-ergodic, and partially observable. We show that Thompson sampling learns the environment class in the sense that (1) asymptotically its …

Logit distance bounds representational similarity of models.

Aggregation distorts causal discovery results but recovery is possible with partial linearity or prior.

A probabilistic query may not be estimable from observed data corrupted by missing values if the data are not missing at random (MAR). It is therefore of theoretical interest and practical importance to determine in principle whether a probabilistic query is estimable from missing data or not when the data are not MAR.…

The paper learns particle swarming models from data using Gaussian processes.

Study uses Bayes Hilbert framework to recover probability measure flows from sensors.

Improves sparse recovery with non-linear Fourier features.

We give a topological model for a polynomial map from $\C^n$ to $\C$ in the neighborhood of a fiber with isolated singularities. This is motivated out of the ``unfolding of links'' described earlier by the first author and Lee Rudolph. The topological model gives a useful encoding of the local and global monodromy for …

Consider a noisy linear observation model with an unknown permutation, based on observing $y = Π^* A x^* + w$, where $x^* \in \mathbb{R}^d$ is an unknown vector, $Π^*$ is an unknown $n \times n$ permutation matrix, and $w \in \mathbb{R}^n$ is additive Gaussian noise. We analyze the problem of permutation recovery in a …

We revisit the problem of robust principal component analysis with features acting as prior side information. To this aim, a novel, elegant, non-convex optimization approach is proposed to decompose a given observation matrix into a low-rank core and the corresponding sparse residual. Rigorous theoretical analysis of t…

All DeFi markets are essentially CFMMs with increasing invariants.

K-means fails catastrophically in high dimensions, Hartigan's avoids it.

We establish a foundation for multivariate counterfactual identification using dynamic optimal transport.

Researchers attempt to categorify biquandle brackets using Khovanov homology methods.

Network growth processes can be understood as generative models of the structure and history of complex networks. This point of view naturally leads to the problem of network archaeology: reconstructing all the past states of a network from its structure---a difficult permutation inference problem. In this paper, we in…

Robust tensor recovery plays an instrumental role in robustifying tensor decompositions for multilinear data analysis against outliers, gross corruptions and missing values and has a diverse array of applications. In this paper, we study the problem of robust low-rank tensor recovery in a convex optimization framework,…

GNMR controls runtime stability in low-precision language model training.

Khovanov homology distinguishes exotic 4-manifolds.

Learning optimal dictionaries for sparse coding has exposed characteristic sparse features of many natural signals. However, universal guarantees of the stability of such features in the presence of noise are lacking. Here, we provide very general conditions guaranteeing when dictionaries yielding the sparsest encoding…

Proposes PA-DSL for correcting noisy human labels in automated data labeling.

Study shows DNNs can recover functions with fewer samples than model parameters at overparameterization.

Study determines minimal surfaces from boundary data, proving topological and conformal recoverability.

New algorithm recovers communities in broader network models.

Analyzes how financial network dependencies can lead to multiple equilibrium outcomes and optimal bailout strategies.

Axiomatizes the bid-ask market maker's quoting rule

This work studies the strong duality of non-convex matrix factorization problems: we show that under certain dual conditions, these problems and its dual have the same optimum. This has been well understood for convex optimization, but little was known for non-convex problems. We propose a novel analytical framework an…

CPFM integrates dimensionality reduction and reconstruction with flow networks.

Deep Convolutional Sparse Coding (D-CSC) is a framework reminiscent of deep convolutional neural networks (DCNNs), but by omitting the learning of the dictionaries one can more transparently analyse the role of the activation function and its ability to recover activation paths through the layers. Papyan, Romano, and E…

This paper presents the first theoretical results showing that stable identification of overcomplete $μ$-coherent dictionaries $Φ\in \mathbb{R}^{d\times K}$ is locally possible from training signals with sparsity levels $S$ up to the order $O(μ^{-2})$ and signal to noise ratios up to $O(\sqrt{d})$. In particular the di…

A new diffusion model improves time-series forecasting by preserving seasonal patterns.

LEAP identifies latent causal variables from temporal data.

This research tackles sample complexity in causal graph recovery with temporal heterogeneity.

Causal Imitation Learning handles noisy measurements and distribution shifts.

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 …

This paper considers the problem of estimating an unknown high dimensional signal from noisy linear measurements, {when} the signal is assumed to possess a \emph{group-sparse} structure in a {known,} fixed dictionary. We consider signals generated according to a natural probabilistic model, and establish new conditions…

We develop a mean-field theory for multi-component ICA in high dimensions.

New method improves robustness of large models without sacrificing accuracy.

Framework selects real estate redevelopment uses by integrating value, risk, complexity, and irreversibility.

Study dynamic equilibrium with insider and general uninformed agent preferences.

In dictionary learning, also known as sparse coding, the algorithm is given samples of the form $y = Ax$ where $x\in \mathbb{R}^m$ is an unknown random sparse vector and $A$ is an unknown dictionary matrix in $\mathbb{R}^{n\times m}$ (usually $m > n$, which is the overcomplete case). The goal is to learn $A$ and $x$. T…

New method for separating mixed signals with nonlinear functions.