Related papers: SOS-based Modal Decomposition on Nondeterministic …
This brief paper develops a probability density that models processes for which the physical mechanism is unknown. It has desirable properties which are not realized by densities derived from Gaussian process or other classic methods. In…
Bisimulation is crucial for verifying process equivalence in probabilistic systems. This paper presents a novel logical framework for analyzing bisimulation in probabilistic parameterized systems, namely, infinite families of finite-state…
Foundation models, such as large language models, have demonstrated success in addressing various language and image processing tasks. In this work, we introduce a multi-modal foundation model for scientific problems, named PROSE-PDE. Our…
In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constructions of objects with such properties are often very difficult, or…
We provide a generalization of the normal mode decomposition for non-symmetric or locality constrained situations. This allows for instance to locally decouple a bipartitioned collection of arbitrarily correlated oscillators up to…
Semantic composition remains an open problem for vector space models of semantics. In this paper, we explain how the probabilistic graphical model used in the framework of Functional Distributional Semantics can be interpreted as a…
Since the rise of fair machine learning as a critical field of inquiry, many different notions on how to quantify and measure discrimination have been proposed in the literature. Some of these notions, however, were shown to be mutually…
Methods for sequential decision-making are often built upon a foundational assumption that the underlying decision process is stationary. This limits the application of such methods because real-world problems are often subject to changes…
One of the fundamental challenges found throughout the data sciences is to explain why things happen in specific ways, or through which mechanisms a certain variable $X$ exerts influences over another variable $Y$. In statistics and machine…
When analyzing probabilistic computations, a powerful approach is to first find a martingale---an expression on the program variables whose expectation remains invariant---and then apply the optional stopping theorem in order to infer…
We give $\operatorname{CMSO}$-transductions that, given a graph $G$, output its modular decomposition, its split decomposition and its bi-join decomposition. This improves results by Courcelle [Logical Methods in Computer Science, 2006] who…
We present an approach to construct approximate Koopman-type decompositions for dynamical systems depending on static or time-varying parameters. Our method simultaneously constructs an invariant subspace and a parametric family of…
We propose a novel method for estimating nonseparable selection models. We show that, for a given selection function, the potential outcome distributions are nonparametrically identified from the selected outcome distributions and can be…
Bayesian optimization (BO) has proven to be an effective paradigm for the global optimization of expensive-to-sample systems. One of the main advantages of BO is its use of Gaussian processes (GPs) to characterize model uncertainty which…
This paper deals with the probabilistic behaviours of distributed systems described by a process calculus considering both probabilistic internal choices and nondeterministic external choices. For this calculus we define and study a typing…
In this paper, we propose an equation-based parametric Reduced Order Model (ROM), whose accuracy is improved with data-driven terms added into the reduced equations. These additions have the aim of reintroducing contributions that in…
It is natural that we can extend Structural Operational Semantics (SOS) to SOS for true concurrency. From SOS to SOS for true concurrency, it is in nature to give the related concepts in SOS a truly concurrent semantics foundation, i.e., a…
In this article we study different aspects of Hermitian operators applying the concept of positive decompositions. On the one hand, we characterize the positivity of an Hermitian operator by means of a norm condition where the factors of…
Conditioning, the central operation in Bayesian statistics, is formalised by the notion of disintegration of measures. However, due to the implicit nature of their definition, constructing disintegrations is often difficult. A folklore…
A key requirement on any well-behaved process language is its compositionality: behavioural equivalence of processes should be respected by the constructors of the language. Turi and Plotkin's abstract GSOS provides an elegant bialgebraic…