A confirmation bias in perceptual decision-making due to hierarchical approximate inference

Making good decisions requires updating beliefs according to new evidence. This is a dynamical process that is prone to biases: in some cases, beliefs become entrenched and resistant to new evidence (leading to primacy effects), while in other cases, beliefs fade over time and rely primarily on later evidence (leading to recency effects). How and why either type of bias dominates in a given context is an important open question. Here, we study this question in classic perceptual decision-making tasks, where, puzzlingly, previous empirical studies differ in the kinds of biases they observe, ranging from primacy to recency, despite seemingly equivalent tasks. We present a new model, based on hierarchical approximate inference and derived from normative principles, that not only explains both primacy and recency effects in existing studies, but also predicts how the type of bias should depend on the statistics of stimuli in a given task. We verify this prediction in a novel visual discrimination task with human observers, finding that each observer’s temporal bias changed as the result of changing the key stimulus statistics identified by our model. The key dynamic that leads to a primacy bias in our model is an overweighting of new sensory information that agrees with the observer’s existing belief—a type of ‘confirmation bias’. By fitting an extended drift-diffusion model to our data we rule out an alternative explanation for primacy effects due to bounded integration. Taken together, our results resolve a major discrepancy among existing perceptual decision-making studies, and suggest that a key source of bias in human decision-making is approximate hierarchical inference.

Approximate Inference for Neural Probabilistic Logic Programming

DeepProbLog is a neural-symbolic framework that integrates probabilistic logic programming and neural networks. It is realized by providing an interface between the probabilistic logic and the neural networks. Inference in probabilistic neural symbolic methods is hard, since it combines logical theorem proving with probabilistic inference and neural network evaluation. In this work, we make the inference more efficient by extending an approximate inference algorithm from the field of statistical-relational AI. Instead of considering all possible proofs for a certain query, the system searches for the best proof. However, training a DeepProbLog model using approximate inference introduces additional challenges, as the best proof is unknown at the start of training which can lead to convergence towards a local optimum. To be able to apply DeepProbLog on larger tasks, we propose: 1) a method for approximate inference using an A*-like search, called DPLA* 2) an exploration strategy for proving in a neural-symbolic setting, and 3) a parametric heuristic to guide the proof search. We empirically evaluate the performance and scalability of the new approach, and also compare the resulting approach to other neural-symbolic systems. The experiments show that DPLA* achieves a speed up of up to 2-3 orders of magnitude in some cases.

A Memory Constrained Approximate Bayesian Inference Approach Using Incremental Construction of Clique Trees

<div>The complexity of inference using the belief propagation algorithms increases exponentially with the maximum clique size. We describe an approximate inference approach when there are clique size limitations due to memory constraints using incremental construction of clique trees.<br></div>

A Memory Constrained Approximate Bayesian Inference Approach Using Incremental Construction of Clique Trees

<div>The complexity of inference using the belief propagation algorithms increases exponentially with the maximum clique size. We describe an approximate inference approach when there are clique size limitations due to memory constraints using incremental construction of clique trees.<br></div>

Graphical Models of Pandemic

Both COVID-19 and novel pandemics challenge those of us within the modeling community, specifically in establishing suitable relations between lifecycles, scales, and existing methods. Herein we demonstrate transitions between models in space/time, individual-to-community, county-to-city, along with models for the trace beginning with exposure, then to symptom manifest, then to community transmission. To that end, we leverage publicly available data to compose a chain of Graphical Models (GMs) for predicting infection rates across communities, space, and time. We'll anchor our GMs against the more expensive yet state-of-the-art Agent-Based Models (ABMs). Insight obtained from designing novel GMs calibrated to ABMs furnishes reduced, yet reliable surrogates for the end-to-end public health challenge of community contact tracing and transmission. Further, this novel research transcends and synergizes information integration and informatics, leading to an advance in the science of GMs. Cognizance into the data lifecycle using properly coarse-grained modeling will broaden the toolkit available to public health specialists, and hopefully empower governments and health agencies, here and abroad, in addressing the profound challenges in disease and vaccination campaigns confronting us by COVID and future pandemics. In this proof of principle study, focusing on the GM methodology development, we show, first, how static GM of the Ising model type (characterised by pair-wise interaction between nodes related to traffic and communications between nodes representing communities, or census tracts within a given city, and with local infection bias) emerge from a dynamic GM of the Independent Cascade type, introduced and studied in Computer and Networks sciences mainly in the context of the spread of social influences. Second, we formulate the problem of inference in epidemiology as inference problems in the Ising model setting. Specifically, we pose the challenge of computing Conditional A-posteriori Level of Infection (CALI), which provides a quantitative answer to the questions: What is the probability that a given node in the GM (given census tract within the city) becomes infected in the result of injection of the infection at another node, e.g. due to arrival of a super-spreader agent or occurrence of the super-spreader event in the area. To answer the question exactly is not feasible for any realistic size (larger than 30-50 nodes) model. We therefore adopt and develop approximate inference techniques, of the variational and variable elimination types, developed in the GM literature. To demonstrate utility of the methodology, which seems new for the public health application, we build a 123-node model of Seattle, as well as its 10-node and 20-node coarse-grained variants, and then conduct the proof of principles experimental studies. The experiments on the coarse-grained models have helped us to validate the approximate inference by juxtaposing it to the exact inference. The experiments also lead to discovery of interesting and most probably universal phenomena. In particular, we observe (a) a strong sensitivity of CALI to the location of the initial infection, and (b) strong alignment of the resulting infection probability (values of CALI) observed at different nodes in the regimes of moderate interaction between the nodes. We then speculate how these, and other observations drawn from the synthetic experiments, can be extended to a more realistic, data driven setting of actual operation importance. We conclude the manuscript with an extensive discussion of how the methodology should be developed further, both at the level of devising realistic GMs from observational data (and also enhancing it with microscopic ABM modeling and simulations) and also regarding utilisation of the GM inference methodology for more complex problems of the pandemic mitigation and control.