arXiv research

Study finds the cutoff for exact recovery in Gaussian mixture models.

New algorithm recovers sparse measures in polynomial time.

Study optimal portfolio selection with Recovery Average Value at Risk, showing better control over liabilities.

Paper explores exact recovery of communities in weighted graphs using Gaussian and exponential distributions.

BalLOT uses optimal transport for balanced k-means clustering.

New framework extends ICA for non-independent variables, identifying pairwise mean independence.

We introduce the {\it diffusion $K$-means} clustering method on Riemannian submanifolds, which maximizes the within-cluster connectedness based on the diffusion distance. The diffusion $K$-means constructs a random walk on the similarity graph with vertices as data points randomly sampled on the manifolds and edges as …

We study exact recovery conditions for convex relaxations of point cloud clustering problems, focusing on two of the most common optimization problems for unsupervised clustering: $k$-means and $k$-median clustering. Motivations for focusing on convex relaxations are: (a) they come with a certificate of optimality, and…

Paper develops a new algorithm for sparse signal recovery.

SMM improves signal recovery from noisy data.

Hybrid QML model improves recovery rate prediction accuracy.

Manifold embedding algorithms map high-dimensional data down to coordinates in a much lower-dimensional space. One of the aims of dimension reduction is to find intrinsic coordinates that describe the data manifold. The coordinates returned by the embedding algorithm are abstract, and finding their physical or domain-r…

We provide a unified treatment of a broad class of noisy structure recovery problems, known as structured normal means problems. In this setting, the goal is to identify, from a finite collection of Gaussian distributions with different means, the distribution that produced some observed data. Recent work has studied s…

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…

Paper analyzes VI for location-scale families, proving robustness guarantees for mean and correlation recovery.

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

For a certain class of distributions, we prove that the linear programming relaxation of $k$-medoids clustering---a variant of $k$-means clustering where means are replaced by exemplars from within the dataset---distinguishes points drawn from nonoverlapping balls with high probability once the number of points drawn a…

New findings on computational limits for estimating hidden structures.

New method for community detection in sparse directed SBMs with exact recovery guarantees.

Model explains capital allocation and wealth distribution dynamics in a frictional economy.

This paper uses a mean-field game to model stablecoin market dynamics and recovery.

Paper proposes robust compressed sensing using generative models.

A regularized risk minimization procedure for regression function estimation is introduced that achieves near optimal accuracy and confidence under general conditions, including heavy-tailed predictor and response variables. The procedure is based on median-of-means tournaments, introduced by the authors in [8]. It is …

In this paper we modify the model of Itkin, Shcherbakov and Veygman, (2019) (ISV2019), proposed for pricing Quanto Credit Default Swaps (CDS) and risky bonds, in several ways. First, it is known since the Lehman Brothers bankruptcy that the recovery rate could significantly vary right before or at default, therefore, i…

We study the problem of recovering a hidden community of cardinality $K$ from an $n \times n$ symmetric data matrix $A$, where for distinct indices $i,j$, $A_{ij} \sim P$ if $i, j$ both belong to the community and $A_{ij} \sim Q$ otherwise, for two known probability distributions $P$ and $Q$ depending on $n$. If $P={\r…

We empirically test predictability on asset price by using stock selection rules based on maximum drawdown and its consecutive recovery. In various equity markets, monthly momentum- and weekly contrarian-style portfolios constructed from these alternative selection criteria are superior not only in forecasting directio…

XGBoost models estimate oil recovery factors with moderate accuracy.

Paper proposes a new clustering model that preserves cluster recovery with fewer dimensions.

Conditional kernel mean embeddings form an attractive nonparametric framework for representing conditional means of functions, describing the observation processes for many complex models. However, the recovery of the original underlying function of interest whose conditional mean was observed is a challenging inferenc…

KSS method converges and recovers correct clustering under certain conditions.

Proposes a new method for determining LGD discount rates based on cost of capital.

Study reveals how attention helps in signal recovery from sequence models using random matrix theory.

The problem of population recovery refers to estimating a distribution based on incomplete or corrupted samples. Consider a random poll of sample size $n$ conducted on a population of individuals, where each pollee is asked to answer $d$ binary questions. We consider one of the two polling impediments: (a) in lossy pop…

Modern scientific instruments produce vast amounts of data, which can overwhelm the processing ability of computer systems. Lossy compression of data is an intriguing solution, but comes with its own drawbacks, such as potential signal loss, and the need for careful optimization of the compression ratio. In this work, …

Paper tackles phase retrieval with robust gradient descent for noisy data.

New system preserves message meaning in wireless networks, improving data rate.

Auto-Encoders are unsupervised models that aim to learn patterns from observed data by minimizing a reconstruction cost. The useful representations learned are often found to be sparse and distributed. On the other hand, compressed sensing and sparse coding assume a data generating process, where the observed data is g…

The paper analyzes DeepWalk and node2vec for community detection in stochastic blockmodels.

Spectral clustering for geometric graphs achieves strong consistency in community recovery.

This work improves distribution recovery from sparse data using Random Forest implicit regularization.

Improved sample complexity for Gaussian Mixture Models using Pair Correlation Factor.

Spike and Slab priors have been of much recent interest in signal processing as a means of inducing sparsity in Bayesian inference. Applications domains that benefit from the use of these priors include sparse recovery, regression and classification. It is well-known that solving for the sparse coefficient vector to ma…

We study an optimal execution problem in the presence of market impact where the security price follows a geometric Ornstein-Uhlenbeck process, which implies the mean-reverting property, and show that the optimal strategy is a mixture of initial/terminal block liquidation and gradual intermediate liquidation. The mean-…

We introduce a convex approach for mixed linear regression over $d$ features. This approach is a second-order cone program, based on L1 minimization, which assigns an estimate regression coefficient in $\mathbb{R}^{d}$ for each data point. These estimates can then be clustered using, for example, $k$-means. For problem…

We are motivated by problems that arise in a number of applications such as Online Marketing and Explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random variable whose mean is a sparse linear superposition of known patterns. Unlike many co…

In various application areas, networked data is collected by measuring interactions involving some specific set of core nodes. This results in a network dataset containing the core nodes along with a potentially much larger set of fringe nodes that all have at least one interaction with a core node. In many settings, t…

The principal submatrix localization problem deals with recovering a $K\times K$ principal submatrix of elevated mean $μ$ in a large $n\times n$ symmetric matrix subject to additive standard Gaussian noise. This problem serves as a prototypical example for community detection, in which the community corresponds to the …

We derive an arbitrage free relationship between recovery swap rates, digital default swap spreads and conventional CDS spreads, and argue that the fair forward recovery rate used in recovery swaps must contain a convexity premium over the expected recovery value.