相关论文: Deterministic Extractors for Additive Sources

Consider a finite set of sources, each producing i.i.d. observations that follow a unique probability distribution on a finite alphabet. We study the problem of matching a finite set of observed sequences to the set of sources under the…

This paper considers lossy source coding of $n$-dimensional memoryless sources and shows an explicit approximation to the minimum source coding rate required to sustain the probability of exceeding distortion $d$ no greater than $\epsilon$,…

Motivated from the fact that universal source coding on countably infinite alphabets is not feasible, this work introduces the notion of almost lossless source coding. Analog to the weak variable-length source coding problem studied by Han…

Two widely-used computational paradigms for sublinear algorithms are using linear measurements to perform computations on a high dimensional input and using structured queries to access a massive input. Typically, algorithms in the former…

There has been a great deal of work establishing that random linear codes are as list-decodable as uniformly random codes, in the sense that a random linear binary code of rate $1 - H(p) - \epsilon$ is $(p,O(1/\epsilon))$-list-decodable…

In successive refinement of information, the decoder refines its representation of the source progressively as it receives more encoded bits. The rate-distortion region of successive refinement describes the minimum rates required to attain…

Generalized Zeckendorf decompositions are expansions of integers as sums of elements of solutions to recurrence relations. The simplest cases are base-$b$ expansions, and the standard Zeckendorf decomposition uses the Fibonacci sequence.…

In this paper, we continue the study of weak multiplier Hopf algebras. We recall the notions of the source and target maps $\varepsilon_s$ and $\varepsilon_t$, as well as of the source and target algebras. Then we investigate these objects…

Support points summarize a large dataset through a smaller set of representative points that can be used for data operations, such as Monte Carlo integration, without requiring access to the full dataset. In this sense, support points offer…

Generalized linear models are flexible tools for the analysis of diverse datasets, but the classical formulation requires that the parametric component is correctly specified and the data contain no atypical observations. To address these…

Random samples are lossy summaries which allow queries posed over the data to be approximated by applying an appropriate estimator to the sample. The effectiveness of sampling, however, hinges on estimator selection. The choice of…

Post-processing of the raw bits produced by a true random number generator (TRNG) is always necessary when the entropy per bit is insufficient for security applications. In this paper, we derive a tight bound on the output min-entropy of…

Probabilistic language generators are theoretically modeled as discrete stochastic processes, yet standard decoding strategies (Top-k, Top-p) impose static truncation rules that fail to accommodate the dynamic information density of natural…

In Bayesian statistics, improper distributions and finitely additive probabilities (FAPs) are the two main alternatives to proper distributions, i.e. countably additive probabilities. Both of them can be seen as limits of proper…

We study the family of intersection graphs of low density objects in low dimensional Euclidean space. This family is quite general, and includes planar graphs. We prove that such graphs have small separators. Next, we present efficient…

We study deterministic extractors for oblivious bit-fixing sources (a.k.a. resilient functions) and exposure-resilient functions with small min-entropy: of the function's n input bits, k << n bits are uniformly random and unknown to the…

We develop a framework for localized source detection in dynamical systems governed by nonlinear partial differential equations based on first and second-order sensitivity analysis. Building on the standard adjoint formulation, which…

Here, we proposed an improved version of the deterministic random extractors $SEJ$ and $PEJ$ proposed by R. R. Farashahi in \cite{F} in 2009. By using the Mumford's representation of a reduced divisor $D$ of the Jacobian $J(\mathbb{F}_q)$…

Diffusion generative models have emerged as a new challenger to popular deep neural generative models such as GANs, but have the drawback that they often require a huge number of neural function evaluations (NFEs) during synthesis unless…

Predictive inference requires balancing statistical accuracy against informational complexity, yet the choice of complexity measure is usually imposed rather than derived. We treat econometric objects as predictive rules, mappings from…