Related papers: Domains and Random Variables
Learning in non-stationary environments is one of the biggest challenges in machine learning. Non-stationarity can be caused by either task drift, i.e., the drift in the conditional distribution of labels given the input data, or the domain…
Random Projection is a foundational research topic that connects a bunch of machine learning algorithms under a similar mathematical basis. It is used to reduce the dimensionality of the dataset by projecting the data points efficiently to…
The emergent field of probabilistic numerics has thus far lacked clear statistical principals. This paper establishes Bayesian probabilistic numerical methods as those which can be cast as solutions to certain inverse problems within the…
Machine learning methods can be unreliable when deployed in domains that differ from the domains on which they were trained. There are a wide range of proposals for mitigating this problem by learning representations that are ``invariant''…
Since its introduction by J. Karamata, regular variation has evolved from a purely mathematical concept into a cornerstone of theoretical probability and data analysis. It is extensively studied and applied in different areas. Its…
We investigate the two-word Naming Game on two-dimensional random geometric graphs. Studying this model advances our understanding of the spatial distribution and propagation of opinions in social dynamics. A main feature of this model is…
When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp.\ functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by…
We consider deep multivariate models for heterogeneous collections of random variables. In the context of computer vision, such collections may e.g. consist of images, segmentations, image attributes, and latent variables. When developing…
As a rule, a quadratic functional depending on a great number of binary variables has a lot of local minima. One of approaches allowing one to find in averaged deeper local minima is aggregation of binary variables into larger…
Random matrix theory (RMT) is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Most of the proposed generalizations keep the first assumption and violate the second. Recently, several authors presented…
Bayesian networks are directed acyclic graphs representing independence relationships among a set of random variables. A random variable can be regarded as a set of exhaustive and mutually exclusive propositions. We argue that there are…
The theory of large deviations deals with the probabilities of rare events (or fluctuations) that are exponentially small as a function of some parameter, e.g., the number of random components of a system, the time over which a stochastic…
A new method is developed to represent probabilistic relations on multiple random events. Where previously knowledge bases containing probabilistic rules were used for this purpose, here a probability distribution over the relations is…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
The probabilistic investigation on record values and record times of a sequence of random variables defined on the same probability space has received much attention from 1952 to now. A great deal of such theory focused on \textit{iid} or…
Supervised learning results typically rely on assumptions of i.i.d. data. Unfortunately, those assumptions are commonly violated in practice. In this work, we tackle such problem by focusing on domain generalization: a formalization where…
Quantum theory is a probabilistic theory with fixed causal structure. General relativity is a deterministic theory but where the causal structure is dynamic. It is reasonable to expect that quantum gravity will be a probabilistic theory…
Causal Learning has emerged as a major theme of research in statistics and machine learning in recent years, promising specific computational techniques to apply to datasets that reveal the true nature of cause and effect in a number of…
It is often stated that quantum mechanics only makes statistical predictions and that a quantum state is described by the various probability distributions associated with it. Can we describe a quantum state completely in terms of…
Decisions are often based on imprecise, uncertain or vague information. Likewise, the consequences of an action are often equally unpredictable, thus putting the decision maker into a twofold jeopardy. Assuming that the effects of an action…