Testing and Improving the Robustness of Amortized Bayesian Inference for Cognitive Models

Contaminant observations and outliers often cause problems when estimating the parameters of cognitive models, which are statistical models representing cognitive processes. In this study, we test and improve the robustness of parameter estimation using amortized Bayesian inference (ABI) with neural networks. To this end, we conduct systematic analyses on a toy example and analyze both synthetic and real data using a popular cognitive model, the Drift Diffusion Models (DDM). First, we study the sensitivity of ABI to contaminants with tools from robust statistics: the empirical influence function and the breakdown point. Next, we propose a data augmentation or noise injection approach that incorporates a contamination distribution into the data-generating process during training. We examine several candidate distributions and evaluate their performance and cost in terms of accuracy and efficiency loss relative to a standard estimator. Introducing contaminants from a Cauchy distribution during training considerably increases the robustness of the neural density estimator as measured by bounded influence functions and a much higher breakdown point. Overall, the proposed method is straightforward and practical to implement and has a broad applicability in fields where outlier detection or removal is challenging.

Abstract Visual Reasoning: An Algebraic Approach for Solving Raven's Progressive Matrices

We introduce algebraic machine reasoning, a new reasoning framework that is well-suited for abstract reasoning. Effectively, algebraic machine reasoning reduces the difficult process of novel problem-solving to routine algebraic computation. The fundamental algebraic objects of interest are the ideals of some suitably initialized polynomial ring. We shall explain how solving Raven's Progressive Matrices (RPMs) can be realized as computational problems in algebra, which combine various well-known algebraic subroutines that include: Computing the Gr\"obner basis of an ideal, checking for ideal containment, etc. Crucially, the additional algebraic structure satisfied by ideals allows for more operations on ideals beyond set-theoretic operations. Our algebraic machine reasoning framework is not only able to select the correct answer from a given answer set, but also able to generate the correct answer with only the question matrix given. Experiments on the I-RAVEN dataset yield an overall $93.2\%$ accuracy, which significantly outperforms the current state-of-the-art accuracy of $77.0\%$ and exceeds human performance at $84.4\%$ accuracy.

How Robust are Limit Order Book Representations under Data Perturbation?

The success of machine learning models in the financial domain is highly reliant on the quality of the data representation. In this paper, we focus on the representation of limit order book data and discuss the opportunities and challenges for learning representations of such data. We also experimentally analyse the issues associated with existing representations and present a guideline for future research in this area.