arXiv research

Active seriation recovers item order from noisy pairwise similarity measurements.

We present a class of macroscopic models of the Limit Order Book to simulate the aggregate behaviour of market makers in response to trading flows. The resulting models are solved numerically and asymptotically, and a class of similarity solutions linked to order book formation and recovery is explored. The main result…

Paper explores limits of high-order clustering with planted structures.

In the present paper, we study the optimal execution problem under stochastic price recovery based on limit order book dynamics. We model price recovery after execution of a large order by accelerating the arrival of the refilling order, which is defined as a Cox process whose intensity increases by the degree of the m…

We propose and analyze a generic method for community recovery in stochastic block models and degree corrected block models. This approach can exactly recover the hidden communities with high probability when the expected node degrees are of order $\log n$ or higher. Starting from a roughly correct community partition …

New framework uses score-based priors to solve ill-conditioned polynomial equations, improving signal recovery from noisy data.

We recover the higher order terms for the acoustic wave equation from measurements of the modulus of the solution. The recovery of these coefficients is reduced to a question of stability for inverting a Hamiltonian flow transform, not the geodesic X-ray transform encountered in other inverse boundary problems like the…

Higher-order tensors can represent scores in a rating system, frames in a video, and images of the same subject. In practice, the measurements are often highly quantized due to the sampling strategies or the quality of devices. Existing works on tensor recovery have focused on data losses and random noises. Only a few …

While defaults are rare events, losses can be substantial even for credit portfolios with a large number of contracts. Therefore, not only a good evaluation of the probability of default is crucial, but also the severity of losses needs to be estimated. The recovery rate is often modeled independently with regard to th…

WARPd method solves inverse problems with approximate sharpness conditions.

The paper improves conditions for unique recovery in homomorphic sensing of subspaces.

New method recovers matrices with nonlinear structures using optimization on Grassmann manifold.

Study recovers spike order in noisy tensor estimation without SNR assumptions.

We investigate the sample size requirement for exact recovery of a high order tensor of low rank from a subset of its entries. In the Tucker decomposition framework, we show that the Riemannian optimization algorithm with initial value obtained from a spectral method can reconstruct a tensor of size $n\times n \times\c…

Nonconvex matrix recovery is known to contain no spurious local minima under a restricted isometry property (RIP) with a sufficiently small RIP constant $δ$. If $δ$ is too large, however, then counterexamples containing spurious local minima are known to exist. In this paper, we introduce a proof technique that is capa…

The current research on credit risk is primarily focused on modeling default probabilities. Recovery rates are often treated as an afterthought; they are modeled independently, in many cases they are even assumed constant. This is despite of their pronounced effect on the tail of the loss distribution. Here, we take a …

StrTransformer recovers sources without labels by optimizing latent matrices and enforcing structural constraints.

We introduce an infectious default and recovery model for N obligors. Obligors are assumed to be exchangeable and their states are described by N Bernoulli random variables S_{i} (i=1,...,N). They are expressed by multiplying independent Bernoulli variables X_{i},Y_{ij},Y'_{ij}, and default and recovery infections are …

Two methods improve tensor recovery in Ising models, revealing gene interactions.

New method improves traffic data recovery for streaming data.

Sharp global guarantees for noisy overparameterized low-rank recovery.

Nonnegative low-rank matrix recovery can have spurious local minima.

Study reveals efficient recovery of multi-modal signals via Bayesian methods and sequential learning.

Tensors play a central role in many modern machine learning and signal processing applications. In such applications, the target tensor is usually of low rank, i.e., can be expressed as a sum of a small number of rank one tensors. This motivates us to consider the problem of low rank tensor recovery from a class of lin…

Suppose that we observe noisy linear measurements of an unknown signal that can be modeled as the sum of two component signals, each of which arises from a nonlinear sub-manifold of a high dimensional ambient space. We introduce SPIN, a first order projected gradient method to recover the signal components. Despite the…

New method tackles non-smooth tensor data for better recovery.

In this paper, we study the recovery of a signal from a set of noisy linear projections (measurements), when such projections are unlabeled, that is, the correspondence between the measurements and the set of projection vectors (i.e., the rows of the measurement matrix) is not known a priori. We consider a special case…

We consider optimal execution strategies for block market orders placed in a limit order book (LOB). We build on the resilience model proposed by Obizhaeva and Wang (2005) but allow for a general shape of the LOB defined via a given density function. Thus, we can allow for empirically observed LOB shapes and obtain a n…

Paper solves recovery of parametrizations from Legendre data.

Estimates multiple related causal graphs with shared causal order.

In this paper, we propose a general framework for sparse and low-rank tensor estimation from cubic sketchings. A two-stage non-convex implementation is developed based on sparse tensor decomposition and thresholded gradient descent, which ensures exact recovery in the noiseless case and stable recovery in the noisy cas…

A new method for efficient causal structure learning at scale.

We study the information-theoretic lower bound of the sample complexity of the correct recovery of diffusion network structures. We introduce a discrete-time diffusion model based on the Independent Cascade model for which we obtain a lower bound of order $Ω(k \log p)$, for directed graphs of $p$ nodes, and at most $k$…

In recent years, a class of dictionaries have been proposed for multidimensional (tensor) data representation that exploit the structure of tensor data by imposing a Kronecker structure on the dictionary underlying the data. In this work, a novel algorithm called "STARK" is provided to learn Kronecker structured dictio…

The completion of tensors, or high-order arrays, attracts significant attention in recent research. Current literature on tensor completion primarily focuses on recovery from a set of uniformly randomly measured entries, and the required number of measurements to achieve recovery is not guaranteed to be optimal. In add…

New method beats volumetric barrier for manifold recovery.

Paper finds exact recovery threshold in general hypergraph model.

Study reveals issues with neural autoregressive models and proposes mode recovery cost.

Motivated by applications such as discovering strong ties in social networks and assembling genome subsequences in biology, we study the problem of recovering a hidden $2k$-nearest neighbor (NN) graph in an $n$-vertex complete graph, whose edge weights are independent and distributed according to $P_n$ for edges in the…

The paper explores the problem of \emph{spectral compressed sensing}, which aims to recover a spectrally sparse signal from a small random subset of its $n$ time domain samples. The signal of interest is assumed to be a superposition of $r$ multi-dimensional complex sinusoids, while the underlying frequencies can assum…

Paper models graph edge dependencies using latent variables for community detection.

Study shows generative priors improve rank-one matrix recovery with optimal sample complexity.

This paper sets thresholds for recovering vertex correspondences in partially correlated graphs.

Study on Gaussian-width complexity on statistical manifolds and its applications in learning and recovery.

In the context of sparse recovery, it is known that most of existing regularizers such as $\ell_1$ suffer from some bias incurred by some leading entries (in magnitude) of the associated vector. To neutralize this bias, we propose a class of models with partial regularizers for recovering a sparse solution of a linear …

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…

New tensor recovery method improves efficiency under strict complementarity.

Adaptive IP approach optimizes intervention design for causal graph recovery.