Related papers: Mathematical Foundations for a Compositional Accou…
From the Bayesian perspective, the category of conditional probabilities (a variant of the Kleisli category of the Giry monad, whose objects are measurable spaces and arrows are Markov kernels) gives a nice framework for conceptualization…
Causal discovery is crucial for understanding complex systems and informing decisions. While observational data can uncover causal relationships under certain assumptions, it often falls short, making active interventions necessary. Current…
Compositional explanations are a family of methods that aim to describe the spatial alignment between neurons' receptive field activations and concepts through logical rules, typically computed via a search over all possible concept…
We present an exact Bayesian inference method for inferring posterior distributions encoded by probabilistic programs featuring possibly unbounded loops. Our method is built on a denotational semantics represented by probability generating…
Compositionality is a key property for dealing with complexity, which has been studied from many points of view in diverse fields. Particularly, the composition of individual computations (or programs) has been widely studied almost since…
Machine learning algorithms have achieved superhuman performance in specific complex domains. However, learning online from few examples and compositional learning for efficient generalization across domains remain elusive. In humans, such…
Functional data are defined as realizations of random functions (mostly smooth functions) varying over a continuum, which are usually collected with measurement errors on discretized grids. In order to accurately smooth noisy functional…
This thesis is about the problem of compositionality in distributional semantics. Distributional semantics presupposes that the meanings of words are a function of their occurrences in textual contexts. It models words as distributions over…
We develop a fully Bayesian framework for function-on-scalars regression with many predictors. The functional data response is modeled nonparametrically using unknown basis functions, which produces a flexible and data-adaptive functional…
The ability to continually learn, retain and deploy skills to accomplish goals is a key feature of intelligent and efficient behavior. However, the neural mechanisms facilitating the continual learning and flexible (re-)composition of…
Sequential experimental design to discover interventions that achieve a desired outcome is a key problem in various domains including science, engineering and public policy. When the space of possible interventions is large, making an…
Compositional Game Theory is a new, recently introduced model of economic games based upon the computer science idea of compositionality. In it, complex and irregular games can be built up from smaller and simpler games, and the equilibria…
Inspired by empirical work in neuroscience for Bayesian approaches to brain function, we give a unified probabilistic account of various types of symbolic reasoning from data. We characterise them in terms of formal logic using the…
Vector space models have become popular in distributional semantics, despite the challenges they face in capturing various semantic phenomena. We propose a novel probabilistic framework which draws on both formal semantics and recent…
Understanding the information processing roles of cortical circuits is an outstanding problem in neuroscience and artificial intelligence. The theoretical setting of Bayesian inference has been suggested as a framework for understanding…
This paper investigates a representation language with flexibility inspired by probabilistic logic and compactness inspired by relational Bayesian networks. The goal is to handle propositional and first-order constructs together with…
We present a new approach for inference in Bayesian networks, which is mainly based on partial differentiation. According to this approach, one compiles a Bayesian network into a multivariate polynomial and then computes the partial…
We present a Bayesian approach for modeling multivariate, dependent functional data. To account for the three dominant structural features in the data--functional, time dependent, and multivariate components--we extend hierarchical dynamic…
Categories of polymorphic lenses in computer science, and of open games in compositional game theory, have a curious structure that is reminiscent of compact closed categories, but differs in some crucial ways. Specifically they have a…
Circuits based on sum-product structure have become a ubiquitous representation to compactly encode knowledge, from Boolean functions to probability distributions. By imposing constraints on the structure of such circuits, certain inference…