相关论文: A note on strong-consistency of componentwise ARH(…

We investigate the modeling and the numerical solution of machine learning problems with prediction functions which are linear combinations of elements of a possibly infinite-dimensional dictionary. We propose a novel flexible composite…

Spectral estimators are fundamental in lowrank matrix models and arise throughout machine learning and statistics, with applications including network analysis, matrix completion and PCA. These estimators aim to recover the leading…

We study the convergence of a drift implicit scheme for one-dimensional SDEs that was considered by Alfonsi for the Cox-Ingersoll-Ross (CIR) process. Under general conditions, we obtain a strong convergence of order 1. In the CIR case,…

The modern definition of optical coherence highlights a frequency dependent function based on a matrix of spectra and cross-spectra. Due to general properties of matrices, such a function is invariant in changes of basis. In this article,…

We consider nonparametric estimation for functional autoregressive processes with Markov switching. First, we study the case where complete data is available; i.e. when we observe the Markov switching regime. Then we estimate the regression…

Transports preserving the angle between two contravariant vector fields but changing their lengths proportional to their own lengths are introduced as `conformal' transports and investigated over spaces with one affine connection and…

We prove that if A and B are bounded self-adjoint operators such that A-B belongs to the trace class, then |A| -|B| belongs to the principal ideal L_{1,\infty} in the algebra L(H) of all bounded operators on an infinite-dimensional Hilbert…

In a Hilbert framework, we consider an inertial Tikhonov regularized dynamical system governed by a maximally comonotone operator, where the damping coefficient is proportional to the square root of the Tikhonov regularization parameter.…

Given an irreducible representation of a group G, we show that all the covariant positive operator valued measures based on G/Z, where Z is a central subgroup, are described by trace class, trace one positive operators.

We improve a phase retrieval approach that uses correlation-based measurements with compactly supported measurement masks [27]. The improved algorithm admits deterministic measurement constructions together with a robust, fast recovery…

The Eigendecomposition of quadratic forms (symmetric matrices) guaranteed by the spectral theorem is a foundational result in applied mathematics. Motivated by a shared structure found in inferential problems of recent interest---namely…

We study log-concavity properties of real sequences $(a_n)_{n \ge 0}$ satisfying a $d$-th order linear recurrence whose coefficients are linear functions of $n$; the so-called P-recursive (or holonomic) sequences. Writing the recurrence in…

The modeling and prediction of multivariate spatio-temporal data involve numerous challenges. Dimension reduction methods can significantly simplify this process, provided that they account for the complex dependencies between variables and…

It is well-known that the approximate factor models have the rotation indeterminacy. It has been considered that the principal component (PC) estimators estimate some rotations of the true factors and factor loadings, but the rotation…

We study the problem of robust linear regression with response variable corruptions. We consider the oblivious adversary model, where the adversary corrupts a fraction of the responses in complete ignorance of the data. We provide a nearly…

The stability of an Auto-Regressive (AR) time sequence of finite order $L$, is determined by the maximal modulus $r^\star$ among all zeros of its generating polynomial. If $r^\star<1$ then the effect of input and initial conditions decays…

Autoregressive pre-trained models combined with decoding methods have achieved impressive performance on complex reasoning tasks. While mainstream decoding strategies such as beam search can generate plausible candidate sets, they often…

Existing causal inference (CI) models are often restricted to data with low-dimensional confounders and singleton actions. We propose an autoregressive (AR) CI framework capable of handling complex confounders and sequential actions…

We give rates of convergence in the strong invariance principle for stationary sequences satisfying some projective criteria. The conditions are expressed in terms of conditional expectations of partial sums of the initial sequence. Our…

Despite a lack of theoretical understanding, deep neural networks have achieved unparalleled performance in a wide range of applications. On the other hand, shallow representation learning with component analysis is associated with rich…