arXiv subjects

Pedro Zuidberg Dos Martires

Publications and source records attributed to Pedro Zuidberg Dos Martires.

26 records · Page 2Linked to original sources

arXiv2023

Differentiable Sampling of Categorical Distributions Using the CatLog-Derivative Trick

Categorical random variables can faithfully represent the discrete and uncertain aspects of data as part of a discrete latent variable model. Learning in such models necessitates taking gradients with respect to the parameters of the categorical probability distributions, which is often intractable due to their combinatorial nature. A popular technique to estimate these otherwise intractable gradients is the Log-Derivative trick. This trick forms the basis of the well-known REINFORCE gradient estimator and its many extensions. While the Log-Derivative trick allows us to differentiate through samples drawn from categorical distributions, it does not take into account the discrete nature of the distribution itself. Our first contribution addresses this shortcoming by introducing the CatLog-Derivative trick - a variation of the Log-Derivative trick tailored towards categorical distributions. Secondly, we use the CatLog-Derivative trick to introduce IndeCateR, a novel and unbiased gradient estimator for the important case of products of independent categorical distributions with provably lower variance than REINFORCE. Thirdly, we empirically show that IndeCateR can be efficiently implemented and that its gradient estimates have significantly lower bias and variance for the same number of samples compared to the state of the art.

cs.LG↗

arXiv2023

Neural Probabilistic Logic Programming in Discrete-Continuous Domains

Neural-symbolic AI (NeSy) allows neural networks to exploit symbolic background knowledge in the form of logic. It has been shown to aid learning in the limited data regime and to facilitate inference on out-of-distribution data. Probabilistic NeSy focuses on integrating neural networks with both logic and probability theory, which additionally allows learning under uncertainty. A major limitation of current probabilistic NeSy systems, such as DeepProbLog, is their restriction to finite probability distributions, i.e., discrete random variables. In contrast, deep probabilistic programming (DPP) excels in modelling and optimising continuous probability distributions. Hence, we introduce DeepSeaProbLog, a neural probabilistic logic programming language that incorporates DPP techniques into NeSy. Doing so results in the support of inference and learning of both discrete and continuous probability distributions under logical constraints. Our main contributions are 1) the semantics of DeepSeaProbLog and its corresponding inference algorithm, 2) a proven asymptotically unbiased learning algorithm, and 3) a series of experiments that illustrate the versatility of our approach.

cs.AI↗

arXiv2021

Measure Theoretic Weighted Model Integration

Weighted model counting (WMC) is a popular framework to perform probabilistic inference with discrete random variables. Recently, WMC has been extended to weighted model integration (WMI) in order to additionally handle continuous variables. At their core, WMI problems consist of computing integrals and sums over weighted logical formulas. From a theoretical standpoint, WMI has been formulated by patching the sum over weighted formulas, which is already present in WMC, with Riemann integration. A more principled approach to integration, which is rooted in measure theory, is Lebesgue integration. Lebesgue integration allows one to treat discrete and continuous variables on equal footing in a principled fashion. We propose a theoretically sound measure theoretic formulation of weighted model integration, which naturally reduces to weighted model counting in the absence of continuous variables. Instead of regarding weighted model integration as an extension of weighted model counting, WMC emerges as a special case of WMI in our formulation.

cs.AI↗

arXiv2020

Symbolic Learning and Reasoning with Noisy Data for Probabilistic Anchoring

Robotic agents should be able to learn from sub-symbolic sensor data, and at the same time, be able to reason about objects and communicate with humans on a symbolic level. This raises the question of how to overcome the gap between symbolic and sub-symbolic artificial intelligence. We propose a semantic world modeling approach based on bottom-up object anchoring using an object-centered representation of the world. Perceptual anchoring processes continuous perceptual sensor data and maintains a correspondence to a symbolic representation. We extend the definitions of anchoring to handle multi-modal probability distributions and we couple the resulting symbol anchoring system to a probabilistic logic reasoner for performing inference. Furthermore, we use statistical relational learning to enable the anchoring framework to learn symbolic knowledge in the form of a set of probabilistic logic rules of the world from noisy and sub-symbolic sensor input. The resulting framework, which combines perceptual anchoring and statistical relational learning, is able to maintain a semantic world model of all the objects that have been perceived over time, while still exploiting the expressiveness of logical rules to reason about the state of objects which are not directly observed through sensory input data. To validate our approach we demonstrate, on the one hand, the ability of our system to perform probabilistic reasoning over multi-modal probability distributions, and on the other hand, the learning of probabilistic logical rules from anchored objects produced by perceptual observations. The learned logical rules are, subsequently, used to assess our proposed probabilistic anchoring procedure. We demonstrate our system in a setting involving object interactions where object occlusions arise and where probabilistic inference is needed to correctly anchor objects.

cs.AI↗

arXiv2020

Monte Carlo Anti-Differentiation for Approximate Weighted Model Integration

Probabilistic inference in the hybrid domain, i.e. inference over discrete-continuous domains, requires tackling two well known #P-hard problems 1)~weighted model counting (WMC) over discrete variables and 2)~integration over continuous variables. For both of these problems inference techniques have been developed separately in order to manage their #P-hardness, such as knowledge compilation for WMC and Monte Carlo (MC) methods for (approximate) integration in the continuous domain. Weighted model integration (WMI), the extension of WMC to the hybrid domain, has been proposed as a formalism to study probabilistic inference over discrete and continuous variables alike. Recently developed WMI solvers have focused on exploiting structure in WMI problems, for which they rely on symbolic integration to find the primitive of an integrand, i.e. to perform anti-differentiation. To combine these advances with state-of-the-art Monte Carlo integration techniques, we introduce \textit{Monte Carlo anti-differentiation} (MCAD), which computes MC approximations of anti-derivatives. In our empirical evaluation we substitute the exact symbolic integration backend in an existing WMI solver with an MCAD backend. Our experiments show that that equipping existing WMI solvers with MCAD yields a fast yet reliable approximate inference scheme.

cs.AI↗

arXiv2019

Learning from Implicit Information in Natural Language Instructions for Robotic Manipulations

Human-robot interaction often occurs in the form of instructions given from a human to a robot. For a robot to successfully follow instructions, a common representation of the world and objects in it should be shared between humans and the robot so that the instructions can be grounded. Achieving this representation can be done via learning, where both the world representation and the language grounding are learned simultaneously. However, in robotics this can be a difficult task due to the cost and scarcity of data. In this paper, we tackle the problem by separately learning the world representation of the robot and the language grounding. While this approach can address the challenges in getting sufficient data, it may give rise to inconsistencies between both learned components. Therefore, we further propose Bayesian learning to resolve such inconsistencies between the natural language grounding and a robot's world representation by exploiting spatio-relational information that is implicitly present in instructions given by a human. Moreover, we demonstrate the feasibility of our approach on a scenario involving a robotic arm in the physical world.

cs.AI↗

arXiv2019

Semantic Relational Object Tracking

This paper addresses the topic of semantic world modeling by conjoining probabilistic reasoning and object anchoring. The proposed approach uses a so-called bottom-up object anchoring method that relies on the rich continuous data from perceptual sensor data. A novel anchoring matching function method learns to maintain object entities in space and time and is validated using a large set of trained humanly annotated ground truth data of real-world objects. For more complex scenarios, a high-level probabilistic object tracker has been integrated with the anchoring framework and handles the tracking of occluded objects via reasoning about the state of unobserved objects. We demonstrate the performance of our integrated approach through scenarios such as the shell game scenario, where we illustrate how anchored objects are retained by preserving relations through probabilistic reasoning.

cs.RO↗

arXiv2018

Knowledge Compilation with Continuous Random Variables and its Application in Hybrid Probabilistic Logic Programming

In probabilistic reasoning, the traditionally discrete domain has been elevated to the hybrid domain encompassing additionally continuous random variables. Inference in the hybrid domain, however, usually necessitates to condone trade-offs on either the inference on discrete or continuous random variables. We introduce a novel approach based on weighted model integration and algebraic model counting that circumvents these trade-offs. We then show how it supports knowledge compilation and exact probabilistic inference. Moreover, we introduce the hybrid probabilistic logic programming language HAL-ProbLog, an extension of ProbLog, to which we apply our inference approach.

cs.AI↗