Related papers: Nonanticipative Rate Distortion Function and Relat…
In this letter, we derive the probability density function (PDF) and cumulative distribution function (CDF) of the minimum of two non-central Chi-square random variables with two degrees of freedom in terms of power series. With the help of…
Kernel methods represent one of the most powerful tools in machine learning to tackle problems expressed in terms of function values and derivatives due to their capability to represent and model complex relations. While these methods show…
Nonuniform Fourier data are routinely collected in applications such as magnetic resonance imaging, synthetic aperture radar, and synthetic imaging in radio astronomy. To acquire a fast reconstruction that does not require an online inverse…
A unified derivation of the off equilibrium fluctuation dissipation relations (FDR) is given for Ising and continous spins to arbitrary order, within the framework of Markovian stochastic dynamics. Knowledge of the FDR allows to develop…
The Random Variable Transformation (RVT) method is a fundamental tool for determining the probability distribution function associated with a Random Variable (RV) Y=g(X), where X is a RV and g is a suitable transformation. In the usual…
We study how the degree of nonlinearity in the input data affects the optimal design of reservoir computers, focusing on how closely the model's nonlinearity should align with that of the data. By reducing minimal RCs to a single tunable…
Deep neural decision forest (NDF) achieved remarkable performance on various vision tasks via combining decision tree and deep representation learning. In this work, we first trace the decision-making process of this model and visualize…
We consider finite approximations of a fractal generated by an iterated function system of affine transformations on $\mathbb{R}^d$ as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a…
The relation between the jump length probability distribution function and the spectral line profile in resonance atomic radiation trapping is considered for Partial Frequency Redistribution (PFR) between absorbed and reemitted radiation.…
Fluctuation theorems (FTs) quantify the thermodynamic reversibility of a system, and for deterministic systems they are defined in terms of the dissipation function. However, in a nonequilibrium steady state of deterministic dynamics, the…
In robust Markov decision processes (RMDPs), it is assumed that the reward and the transition dynamics lie in a given uncertainty set. By targeting maximal return under the most adversarial model from that set, RMDPs address performance…
This paper establishes the theoretical limits of channel state information (CSI) feedback in frequency-division duplexing (FDD) multi-antenna orthogonal frequency-division multiplexing (OFDM) systems under finite-length training with…
A reduced-bias nonparametric estimator of the cumulative distribution function (CDF) and the survival function is proposed using infinite-order kernels. Fourier transform theory on generalized functions is utilized to obtain the improved…
We consider the problem of distributed lossy linear function computation in a tree network. We examine two cases: (i) data aggregation (only one sink node computes) and (ii) consensus (all nodes compute the same function). By quantifying…
This paper describes and motivates a new decision theory known as functional decision theory (FDT), as distinct from causal decision theory and evidential decision theory. Functional decision theorists hold that the normative principle for…
In this article we prove a new central limit theorem (CLT) for coupled particle filters (CPFs). CPFs are used for the sequential estimation of the difference of expectations w.r.t. filters which are in some sense close. Examples include the…
Supervised fine-tuning (SFT) is computationally efficient but often yields inferior generalization compared to reinforcement learning (RL). This gap is primarily driven by RL's use of on-policy data. We propose a framework to bridge this…
Understanding atomic structures is crucial, yet amorphous materials remain challenging due to their irregular and non-periodic nature. The Wavelet Transform Radial Distribution Function (WT-RDF) offers a physics-based framework for…
This paper derives novel results on the characterization of the the causal information rate-distortion function (IRDF) $R_{c}^{it}(D)$ for arbitrarily-distributed one-sided stationary $\kappa$-th order Markov source x(1),x(2),.... It is…
Distributional reinforcement learning (DRL) has achieved empirical success in various domains. One core task in DRL is distributional policy evaluation, which involves estimating the return distribution $\eta^\pi$ for a given policy $\pi$.…