Related papers: Synthetic topology in Homotopy Type Theory for pro…
The ability to generate high-fidelity synthetic data is crucial when available (real) data is limited or where privacy and data protection standards allow only for limited use of the given data, e.g., in medical and financial data-sets.…
We use methods from topological data analysis to study the topological features of certain distributions of string vacua. Topological data analysis is a multi-scale approach used to analyze the topological features of a dataset by…
The estimation of information measures of continuous distributions based on samples is a fundamental problem in statistics and machine learning. In this paper, we analyze estimates of differential entropy in $K$-dimensional Euclidean space,…
We introduce the notion of a template for discrete Morse theory. Templates provide a memory efficient approach to the computation of homological invariants (e.g., homology, persistent homology, Conley complexes) of cell complexes. We…
Statistical models of real world data typically involve continuous probability distributions such as normal, Laplace, or exponential distributions. Such distributions are supported by many probabilistic modelling formalisms, including…
Notions and techniques of enriched category theory can be used to study topological structures, like metric spaces, topological spaces and approach spaces, in the context of topological theories. Recently in [D. Hofmann, Injective spaces…
Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…
We provide a topological classification of locally constant functions over subshifts of finite type via their zero-temperature measures. Our approach is to analyze the relationship between the distribution of the zero-temperature measures…
In 20th century mathematics, the field of topology, which concerns the properties of geometric objects under continuous transformation, has proved surprisingly useful in application to the study of discrete mathematics, such as…
Higher inductive types are a class of type-forming rules, introduced to provide basic (and not-so-basic) homotopy-theoretic constructions in a type-theoretic style. They have proven very fruitful for the "synthetic" development of homotopy…
We present a computational implementation of diagrammatic sets, a model of higher-dimensional diagram rewriting that is "topologically sound": diagrams admit a functorial interpretation as homotopies in cell complexes. This has potential…
We present an approach to deep estimation of discrete conditional probability distributions. Such models have several applications, including generative modeling of audio, image, and video data. Our approach combines two main techniques:…
We describe a Martin-L\"of-style dependent type theory, called Cocon, that allows us to mix the intensional function space that is used to represent higher-order abstract syntax (HOAS) trees with the extensional function space that…
This work proposes a method to evaluate synthetic tabular data generated to augment small sample datasets. While data augmentation techniques can increase sample counts for machine learning applications, traditional validation approaches…
We present a formal model developed to reason about topologies created by sensor ranges. This model is used to formalise the topological aspects of an existing counting algorithm to estimate the number of targets in the area covered by the…
Topology optimization (TO) is a well-established methodology for structural design under user-defined constraints, e.g. minimum volume and maximum stiffness. However, such methods have traditionally been applied to static, deterministic…
Distributionally balanced sampling designs are low-discrepancy probability designs obtained by minimizing the expected discrepancy between the auxiliary-variable distribution of a random sample and the target population distribution.…
We combine Homotopy Type Theory with axiomatic cohesion, expressing the latter internally with a version of "adjoint logic" in which the discretization and codiscretization modalities are characterized using a judgmental formalism of "crisp…
Topological measurements are increasingly being accepted as an important tool for quantifying complex structures. In many applications, these structures can be expressed as nodal domains of real-valued functions and are obtained only…
In local relative $p$-adic Hodge theory, we show that the Galois cohomology of a finite height crystalline representation (up to a twist) is essentially computed via the (Fontaine--Messing) syntomic complex with coefficients in the…