Related papers: Causal Rate Distortion Function on Abstract Alphab…
We improve the existing achievable rate regions for causal and for zero-delay source coding of stationary Gaussian sources under an average mean squared error (MSE) distortion measure. To begin with, we find a closed-form expression for the…
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…
Kernel embeddings have emerged as a powerful tool for representing probability measures in a variety of statistical inference problems. By mapping probability measures into a reproducing kernel Hilbert space (RKHS), kernel embeddings enable…
In this paper, the rate-distortion theory of the Gray-Wyner lossy source coding system is investigated. For the case of jointly Gaussian distributed sources, we establish an expression for the rate-distortion function under the constraint…
Causal reasoning and compositional reasoning are two core aspirations in AI. Measuring the extent of these behaviors requires principled evaluation methods. We explore a unified perspective that considers both behaviors simultaneously,…
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…
In this paper, we introduce a new kernel function which differs from previous functions, and play an important role for generating a new design of primal-dual interior point algorithms for semidefinite linear complementarity problem. Its…
Predicting the effect of interventions with many possible variations, e.g., therapeutic content that affects mental health outcomes or an earnings call transcript that drives movement in share price, is useful across several domains.…
The use of kernels for nonlinear prediction is widespread in machine learning. They have been popularized in support vector machines and used in kernel ridge regression, amongst others. Kernel methods share three aspects. First, instead of…
A new source model, which consists of an intrinsic state part and an extrinsic observation part, is proposed and its information-theoretic characterization, namely its rate-distortion function, is defined and analyzed. Such a source model…
This paper proposes a causal inference relation and causal programming as general frameworks for causal inference with structural causal models. A tuple, $\langle M, I, Q, F \rangle$, is an instance of the relation if a formula, $F$,…
A receiver wants to compute a function of two correlated sources separately observed by two transmitters. One of the transmitters may send a possibly private message to the other transmitter in a cooperation phase before both transmitters…
Kernels are often developed and used as implicit mapping functions that show impressive predictive power due to their high-dimensional feature space representations. In this study, we gradually construct a series of simple feature maps that…
For a number of lossy source coding problems it is shown that even if the usual single-letter sum-rate-distortion expressions may become invalid for non-infinite distortion functions, they can be approached, to any desired accuracy, via the…
We derive quantum counterparts of two key theorems of classical information theory, namely, the rate distortion theorem and the source-channel separation theorem. The rate-distortion theorem gives the ultimate limits on lossy data…
Compared to nonparametric estimators in the multivariate setting, kernel estimators for functional data models have a larger order of bias. This is problematic for constructing confidence regions or statistical tests since the bias might…
I propose kernel ridge regression estimators for nonparametric dose response curves and semiparametric treatment effects in the setting where an analyst has access to a selected sample rather than a random sample; only for select…
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…
We consider the problem of causal effect estimation with an unobserved confounder, where we observe a single proxy variable that is associated with the confounder. Although it has been shown that the recovery of an average causal effect is…
The average treatment effect, which is the difference in expectation of the counterfactuals, is probably the most popular target effect in causal inference with binary treatments. However, treatments may have effects beyond the mean, for…