Related papers: Causal Rate Distortion Function on Abstract Alphab…
We propose causal effect estimators based on empirical Fr\'{e}chet means and operator-valued kernels, tailored to functional data spaces. These methods address the challenges of high-dimensionality, sequential ordering, and model complexity…
Interventional causal models describe several joint distributions over some variables used to describe a system, one for each intervention setting. They provide a formal recipe for how to move between the different joint distributions and…
We prove statistical rates of convergence for kernel-based least squares regression from i.i.d. data using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is related to…
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…
Convolutional Neural Networks (CNNs) are known to be significantly over-parametrized, and difficult to interpret, train and adapt. In this paper, we introduce a structural regularization across convolutional kernels in a CNN. In our…
Organisms have to keep track of the information in the environment that is relevant for adaptive behaviour. Transmitting information in an economical and efficient way becomes crucial for limited-resourced agents living in high-dimensional…
Understanding predictions made by deep neural networks is notoriously difficult, but also crucial to their dissemination. As all machine learning based methods, they are as good as their training data, and can also capture unwanted biases.…
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…
Random feature approximation is arguably one of the most popular techniques to speed up kernel methods in large scale algorithms and provides a theoretical approach to the analysis of deep neural networks. We analyze generalization…
With the widespread application of causal inference, it is increasingly important to have tools which can test for the presence of causal effects in a diverse array of circumstances. In this vein we focus on the problem of testing for…
The functional generalized additive model (FGAM) provides a more flexible nonlinear functional regression model than the well-studied functional linear regression model. This paper restricts attention to the FGAM with identity link and…
We propose a new attribution method for neural networks developed using first principles of causality (to the best of our knowledge, the first such). The neural network architecture is viewed as a Structural Causal Model, and a methodology…
It is generally difficult to make any statements about the expected prediction error in an univariate setting without further knowledge about how the data were generated. Recent work showed that knowledge about the real underlying causal…
The common approach to radial distortion is by the means of polynomial approximation, which introduces distortion-specific parameters into the camera model and requires estimation of these distortion parameters. The task of estimating…
The fragmentation equation is commonly expressed in terms of two functions, the rate of fragmentation and the mean number of fragments. In the case of binary fragmentation an alternative description is possible based on the fragmentation…
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…
We consider parametrized problems driven by spatially nonlocal integral operators with parameter-dependent kernels. In particular, kernels with varying nonlocal interaction radius $\delta > 0$ and fractional Laplace kernels, parametrized by…
Accurate approximations to density functionals have recently been obtained via machine learning (ML). By applying ML to a simple function of one variable without any random sampling, we extract the qualitative dependence of errors on…
A correspondence between database tuples as causes for query answers in databases and tuple-based repairs of inconsistent databases with respect to denial constraints has already been established. In this work, answer-set programs that…
We consider the problem of coding for computing with maximal distortion, where the sender communicates with a receiver, which has its own private data and wants to compute a function of their combined data with some fidelity constraint…