Related papers: Evaluation of the Gilbert-Varshamov Bound using Mu…
We study natural examples of binary channels with synchronization errors. These include the duplication channel, which independently outputs a given bit once or twice, and geometric channels that repeat a given bit according to a geometric…
We propose a general framework for regularization in M-estimation problems under time dependent (absolutely regular-mixing) data which encompasses many of the existing estimators. We derive non-asymptotic concentration bounds for the…
This paper considers the quantization problem on the Grassmann manifold with dimension n and p. The unique contribution is the derivation of a closed-form formula for the volume of a metric ball in the Grassmann manifold when the radius is…
The Information Bottleneck (IB) is a conceptual method for extracting the most compact, yet informative, representation of a set of variables, with respect to the target. It generalizes the notion of minimal sufficient statistics from…
Variational inference is a general approach for approximating complex density functions, such as those arising in latent variable models, popular in machine learning. It has been applied to approximate the maximum likelihood estimator and…
We consider gravitational wave production by bubble collisions during a cosmological first-order phase transition. In the literature, such spectra have been estimated by simulating the bubble dynamics, under so-called thin-wall and envelope…
This paper constructs and studies the Gromov-Witten invariants and their properties for noncompact geometrically bounded symplectic manifolds. Two localization formulas for GW-invariants are also proposed and proved. As applications we get…
The capacity of multiple-input multiple-output additive white Gaussian noise channels is investigated under peak amplitude constraints on the norm of the input vector. New insights on the capacity-achieving input distribution are presented.…
Using Chebyshev polynomials combined with some mild combinatorics, we provide a new formula for the analytical planar limit of a random matrix model with a one-cut potential $V$. For potentials $V(x)=x^{2}/2-\sum_{n\ge1}a_{n}x^{n}/n$, as a…
In this paper we consider the construction of simultaneous confidence bands for the spectral density of a stationary time series using a Gaussian approximation for classical lag-window spectral density estimators evaluated at the set of all…
The stochastic volatility model is a popular tool for modeling the volatility of assets. The model is a nonlinear and non-Gaussian state space model, and consequently is difficult to fit. Many approaches, both classical and Bayesian, have…
The error exponent of Markov channels with feedback is studied in the variable-length block-coding setting. Burnashev's classic result is extended and a single letter characterization for the reliability function of finite-state Markov…
Uncertainty in the estimation of the causal effect in observational studies is often due to unmeasured confounding, i.e., the presence of unobserved covariates linking treatments and outcomes. Instrumental Variables (IV) are commonly used…
We define the Gromov-Witten invariants for the parabolic bundles over an orbifold $C$ in various situation. Those bring us to refine this notion to get an accurate computation of the number of maximal subbundles of a sufficiently general…
We introduce a random coding technique for transmission over discrete memoryless channels, reminiscent of the basic construction attaining the Gilbert-Varshamov bound for codes in Hamming spaces. The code construction is based on drawing…
Using Mathematica package, we derive analytical closed-form expressions for the shear and the bulk viscosity coefficients in multicomponent relativistic gases with constant cross sections, being the relativistic generalization for the hard…
Probabilistic circuits (PCs) enable exact and tractable inference but employ data independent mixture weights that limit their ability to capture local geometry of the data manifold. We propose Voronoi tessellations (VT) as a natural way to…
We survey general properties of multiplicative arithmetic functions of several variables and related convolutions, including the Dirichlet convolution and the unitary convolution. We introduce and investigate a new convolution, called gcd…
Given discrete time observations over a fixed time interval, we study a nonparametric Bayesian approach to estimation of the volatility coefficient of a stochastic differential equation. We postulate a histogram-type prior on the volatility…
As a phase space language for quantum mechanics, the Wigner function approach bears a close analogy to classical mechanics and has been drawing growing attention, especially in simulating quantum many-body systems. However, deterministic…