Learning Comprehensible Theories from Structured Data

This thesis is concerned with the problem of learning comprehensible theories from structured data and covers primarily classification and regression learning. The basic knowledge representation language is set around a polymorphically-typed, higher-order logic. The general setup is closely related to the learning from propositionalized knowledge and learning from interpretations settings in Inductive Logic Programming. Individuals (also called instances) are represented as terms in the logic. A grammar-like construct called a predicate rewrite system is used to define features in the form of predicates that individuals may or may not satisfy. For learning, decision-tree algorithms of various kinds are adopted.¶ The scope of the thesis spans both theory and practice. ..

Declarative programming for agent applications

This paper introduces the execution model of a declarative programming language intended for agent applications. Features supported by the language include functional and logic programming idioms, higher-order functions, modal computation, probabilistic computation, and some theorem-proving capabilities. The need for these features is motivated and examples are given to illustrate the central ideas

Reinforcement Learning via AIXI Approximation

This paper introduces a principled approach for the design of a scalable general reinforcement learning agent. This approach is based on a direct approximation of AIXI, a Bayesian optimality notion for general reinforcement learning agents. Previously, it has been unclear whether the theory of AIXI could motivate the design of practical algorithms. We answer this hitherto open question in the affirmative, by providing the first computationally feasible approximation to the AIXI agent. To develop our approximation, we introduce a Monte Carlo Tree Search algorithm along with an agent-specific extension of the Context Tree Weighting algorithm. Empirically, we present a set of encouraging results on a number of stochastic, unknown, and partially observable domains.Comment: 8 LaTeX pages, 1 figur

Spatially Invariant Unsupervised 3D Object Segmentation with Graph Neural Networks

In this paper, we tackle the problem of unsupervised 3D object segmentation from a point cloud without RGB information. In particular, we propose a framework, SPAIR3D, to model a point cloud as a spatial mixture model and jointly learn the multiple-object representation and segmentation in 3D via Variational Autoencoders (VAE). Inspired by SPAIR, we adopt an object-specification scheme that describes each object's location relative to its local voxel grid cell rather than the point cloud as a whole. To model the spatial mixture model on point clouds, we derive the Chamfer Likelihood, which fits naturally into the variational training pipeline. We further design a new spatially invariant graph neural network to generate a varying number of 3D points as a decoder within our VAE. Experimental results demonstrate that SPAIR3D is capable of detecting and segmenting variable number of objects without appearance information across diverse scenes

Variational Inference for Scalable 3D Object-centric Learning

We tackle the task of scalable unsupervised object-centric representation learning on 3D scenes. Existing approaches to object-centric representation learning show limitations in generalizing to larger scenes as their learning processes rely on a fixed global coordinate system. In contrast, we propose to learn view-invariant 3D object representations in localized object coordinate systems. To this end, we estimate the object pose and appearance representation separately and explicitly map object representations across views while maintaining object identities. We adopt an amortized variational inference pipeline that can process sequential input and scalably update object latent distributions online. To handle large-scale scenes with a varying number of objects, we further introduce a Cognitive Map that allows the registration and query of objects on a per-scene global map to achieve scalable representation learning. We explore the object-centric neural radiance field (NeRF) as our 3D scene representation, which is jointly modeled within our unsupervised object-centric learning framework. Experimental results on synthetic and real datasets show that our proposed method can infer and maintain object-centric representations of 3D scenes and outperforms previous models

Probabilities on Sentences in an Expressive Logic

Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive languages like higher-order logic are ideally suited for representing and reasoning about structured knowledge. Uncertain knowledge can be modeled by using graded probabilities rather than binary truth-values. The main technical problem studied in this paper is the following: Given a set of sentences, each having some probability of being true, what probability should be ascribed to other (query) sentences? A natural wish-list, among others, is that the probability distribution (i) is consistent with the knowledge base, (ii) allows for a consistent inference procedure and in particular (iii) reduces to deductive logic in the limit of probabilities being 0 and 1, (iv) allows (Bayesian) inductive reasoning and (v) learning in the limit and in particular (vi) allows confirmation of universally quantified hypotheses/sentences. We translate this wish-list into technical requirements for a prior probability and show that probabilities satisfying all our criteria exist. We also give explicit constructions and several general characterizations of probabilities that satisfy some or all of the criteria and various (counter) examples. We also derive necessary and sufficient conditions for extending beliefs about finitely many sentences to suitable probabilities over all sentences, and in particular least dogmatic or least biased ones. We conclude with a brief outlook on how the developed theory might be used and approximated in autonomous reasoning agents. Our theory is a step towards a globally consistent and empirically satisfactory unification of probability and logic.Comment: 52 LaTeX pages, 64 definiton/theorems/etc, presented at conference Progic 2011 in New Yor

Context tree switching

This paper describes the Context Tree Switching technique, a modification of Context Tree Weighting for the prediction of binary, stationary, n-Markov sources. By modifying Context Tree Weighting’s recursive weighting scheme, it is possible to mix over a strictly larger class of models without increasing the asymptotic time or space complexity of the original algorithm. We prove that this generalization preserves the desirable theoretical properties of Context Tree Weighting on stationary n-Markov sources, and show empirically that this new technique leads to consistent improvements over Context Tree Weighting as measured on the Calgary Corpus