Related papers: Detection limits in the high-dimensional spiked re…

Although a generalized spike population model has been actively studied in random matrix theory, its application to real data has been rarely explored. We find that most methods for determining the number of spikes based on the Johnstone's…

We consider a spiked random matrix model obtained by applying a function entrywise to a signal-plus-noise symmetric data matrix. We prove that the largest eigenvalue of this model, which we call a transformed spiked Wigner matrix, exhibits…

We analyze the asymptotic behavior and scaling limits of large random matrices rescaled via the Sinkhorn algorithm to match prescribed row and column margins. For a random matrix with independent sub-exponential entries, we show that its…

We study a new parametric approach for particular hidden stochastic models such as the Stochastic Volatility model. This method is based on contrast minimization and deconvolution. After proving consistency and asymptotic normality of the…

We study two spiked models of random matrices under general frameworks corresponding respectively to additive deformation of random symmetric matrices and multiplicative perturbation of random covariance matrices. In both cases, the…

We study parametric inference on a rich class of hazard regression models in the presence of right-censoring. Previous literature has reported some inferential challenges, such as multimodal or flat likelihood surfaces, in this class of…

We study the chaotic behavior of the Gibbs state of spin-glasses under the application of an external magnetic field, in the crossover region where the field intensity scales proportional to $1/\sqrt{N}$, being $N$ the system size. We show…

The boson peak (BP), a low-energy excess in the vibrational density of states over the Debye contribution, is often identified as a characteristic of amorphous solid materials. Despite decades of efforts, its microscopic origin still…

We develop an algorithm for computing bounded reachability probability for hybrid systems, i.e., the probability that the system reaches an unsafe region within a finite number of discrete transitions. In particular, we focus on hybrid…

Hierarchical Bayesian models are increasingly used in large, inhomogeneous complex network dynamical systems by modeling parameters as draws from a hyperparameter-governed distribution. However, theoretical guarantees for these estimates as…

Spectral analysis plays a crucial role in high-dimensional statistics, where determining the asymptotic distribution of various spectral statistics remains a challenging task. Due to the difficulties of deriving the analytic form, recent…

In an earlier work we had considered a Gaussian ensemble of random matrices in the presence of a given external matrix source. The measure is no longer unitary invariant and the usual techniques based on orthogonal polynomials, or on the…

Anomaly detection in medical imaging is a challenging task in contexts where abnormalities are not annotated. This problem can be addressed through unsupervised anomaly detection (UAD) methods, which identify features that do not match with…

Data-driven anomaly detection methods typically build a model for the normal behavior of the target system, and score each data instance with respect to this model. A threshold is invariably needed to identify data instances with high (or…

Consider the spiked Wigner model \[ X = \sum_{i = 1}^k \lambda_i u_i u_i^\top + \sigma G, \] where $G$ is an $N \times N$ GOE random matrix, and the eigenvalues $\lambda_i$ are all spiked, i.e. above the Baik-Ben Arous-P\'ech\'e (BBP)…

We examine the constraints cosmological observations can place on any trans-Planckian corrections to the primordial spectrum of perturbations underlying the anisotropies in the Cosmic Microwave Background. We focus on models of…

Sample correlation matrices are employed ubiquitously in statistics. However, quite surprisingly, little is known about their asymptotic spectral properties for high-dimensional data, particularly beyond the case of "null models" for which…

During recent years the interest of optimization and machine learning communities in high-probability convergence of stochastic optimization methods has been growing. One of the main reasons for this is that high-probability complexity…

Raghavendra (STOC 2008) gave an elegant and surprising result: if Khot's Unique Games Conjecture (STOC 2002) is true, then for every constraint satisfaction problem (CSP), the best approximation ratio is attained by a certain simple…

Robust statistical inference often faces a severe computational-statistical gap when dealing with complex parameter spaces. We investigate minimax signal detection in the Gaussian sequence model under strong $\epsilon$-contamination, where…