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Lifted probabilistic inference (Poole, 2003) and symbolic dynamic programming for lifted stochastic planning (Boutilier et al, 2001) were introduced around the same time as algorithmic efforts to use abstraction in stochastic systems. Over…
We consider a wide class of semi linear Hamiltonian partial differential equa- tions and their approximation by time splitting methods. We assume that the nonlinearity is polynomial, and that the numerical tra jectory remains at least uni-…
Discrete statistical models supported on labelled event trees can be specified using so-called interpolating polynomials which are generalizations of generating functions. These admit a nested representation. A new algorithm exploits the…
Federated Learning (FL) enables collaborative model training across distributed devices while preserving data privacy. Nonetheless, the heterogeneity of edge devices often leads to inconsistent performance of the globally trained models,…
Hybrid continuous-discrete models naturally represent many real-world applications in robotics, finance, and environmental engineering. Inference with large-scale models is challenging because relational structures deteriorate rapidly…
We provide an overview of iterated function systems (IFS), where randomly chosen state-to-state maps are applied iteratively to a state. We aim to summarize the state of art and, where possible, identify fundamental challenges and…
We review aspects of an important paper by Robert Strichartz concerning reverse iterated function systems (i.f.s.) and fractal blowups. We compare the invariant sets of reverse i.f.s. with those of more standard i.f.s. and with those of…
In this paper, we consider the problem of lifted inference in the context of Prism-like probabilistic logic programming languages. Traditional inference in such languages involves the construction of an explanation graph for the query and…
Iterated function systems (IFS) can be a surprisingly useful tool for studying structure in data. Here we present results stemming from a 2013 computational study by the author using IFS. The results include fractal patterns that reveal…
Distributions over rankings are used to model data in a multitude of real world settings such as preference analysis and political elections. Modeling such distributions presents several computational challenges, however, due to the…
Partial observations of continuous time-series dynamics at arbitrary time stamps exist in many disciplines. Fitting this type of data using statistical models with continuous dynamics is not only promising at an intuitive level but also has…
We address the problem of approximating an unknown function from its discrete samples given at arbitrarily scattered sites. This problem is essential in numerical sciences, where modern applications also highlight the need for a solution to…
There has been significant interest in the use of fully-connected graphical models and deep-structured graphical models for the purpose of structured inference. However, fully-connected and deep-structured graphical models have been largely…
We study the statistical capacity of the classical binary perceptrons with general thresholds $\kappa$. After recognizing the connection between the capacity and the bilinearly indexed (bli) random processes, we utilize a recent progress in…
Craig interpolation is a fundamental property of classical and non-classic logics with a plethora of applications from philosophical logic to computer-aided verification. The question of which interpolants can be obtained from an…
Many high dimensional integrals can be reduced to the problem of finding the relative measures of two sets. Often one set will be exponentially larger than the other, making it difficult to compare the sizes. A standard method of dealing…
Existing works on large language model (LLM) decomposition mainly focus on improving performance on downstream tasks, but they ignore the poor parallel inference performance when trying to scale up the model size. To mitigate this important…
The problem of extrapolation and interpolation of asymptotic series is considered. Several new variants of improving the accuracy of the self-similar approximants are suggested. The methods are illustrated by examples typical of chemical…
Various methods for lifted probabilistic inference have been proposed, but our understanding of these methods and the relationships between them is still limited, compared to their propositional counterparts. The only existing theoretical…
Bayesian Filtering for plan and activity recognition is challenging for scenarios that contain many observation equivalent entities (i.e. entities that produce the same observations). This is due to the combinatorial explosion in the number…