Related papers: Causal Rate Distortion Function on Abstract Alphab…
We consider a problem of coding for computing, where the decoder wishes to estimate a function of its local message and the source message at the encoder within a given distortion. We show that the rate-distortion function can be…
We analyse the convergence of sampling algorithms for functions in reproducing kernel Hilbert spaces (RKHS). To this end, we discuss approximation properties of kernel regression under minimalistic assumptions on both the kernel and the…
In this paper, we discuss the convergence analysis of the conjugate gradient-based algorithm for the functional linear model in the reproducing kernel Hilbert space framework, utilizing early stopping results in regularization against…
Random feature maps are used to decrease the computational cost of kernel machines in large-scale problems. The Mondrian kernel is one such example of a fast random feature approximation of the Laplace kernel, generated by a computationally…
The goal of algorithmic recourse is to reverse unfavorable decisions (e.g., from loan denial to approval) under automated decision making by suggesting actionable feature changes (e.g., reduce the number of credit cards). To generate…
In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape…
We discuss, in terms of rate-distortion theory, the fitness of molecular codes as the problem of designing an optimal information channel. The fitness is governed by an interplay between the cost and quality of the channel, which induces…
Causal learning is a beneficial approach to analyze the cause and effect relationships among variables in a dataset. A causal graph can be generated from a dataset using a particular causal algorithm, for instance, the PC algorithm or Fast…
In this paper, we establish minimax optimal rates of convergence for prediction in a semi-functional linear model that consists of a functional component and a less smooth nonparametric component. Our results reveal that the smoother…
Quantum random variable, distortion operator are introduced based on canonical operators. As the lower bound of rate distortion, the entanglement information rate distortion is achieved by Gaussian map for Gaussian source. General Gaussian…
We derive some simple relations that demonstrate how the posterior convergence rate is related to two driving factors: a "penalized divergence" of the prior, which measures the ability of the prior distribution to propose a nonnegligible…
For a discrete memoryless channel with finite input and output alphabets, we prove convergence of a parametric family of iterative computations of the optimal correct-decoding exponent. The exponent, as a function of communication rate, is…
Kernel-based modal statistical methods include mode estimation, regression, and clustering. Estimation accuracy of these methods depends on the kernel used as well as the bandwidth. We study effect of the selection of the kernel function to…
A locally repairable code with availability has the property that every code symbol can be recovered from multiple, disjoint subsets of other symbols of small size. In particular, a code symbol is said to have $(r,t)$-availability if it can…
Causal representation learning seeks to uncover causal relationships among high-level latent variables from low-level, entangled, and noisy observations. Existing approaches often either rely on deep neural networks, which lack…
In this work, we investigate Gaussian process regression used to recover a function based on noisy observations. We derive upper and lower error bounds for Gaussian process regression with possibly misspecified correlation functions. The…
In the successive refinement problem, a fixed-length sequence emitted from an information source is encoded into two codewords by two encoders in order to give two reconstructions of the sequence. One of two reconstructions is obtained by…
Contrastive learning is a powerful framework for learning self-supervised representations that generalize well to downstream supervised tasks. We show that multiple existing contrastive learning methods can be reinterpreted as learning…
The form of Dueck and K\"orner's exponent function for correct decoding probability for discrete memoryless channels at rates above the capacity is similar to the form of Csisz\'ar and K\"orner's exponent function for correct decoding…
Recent advances in Rate-Distortion-Perception (RDP) theory highlight the importance of balancing compression level, reconstruction quality, and perceptual fidelity. While previous work has explored numerical approaches to approximate the…