Amortized Inference for Correlated Discrete Choice Models via Equivariant Neural Networks

Discrete choice models are fundamental tools in management science, economics, and marketing for understanding and predicting decision-making. Logit-based models are dominant in applied work, largely due to their convenient closed-form expressions for choice probabilities. However, these models entail restrictive assumptions on the stochastic utility component, constraining our ability to capture realistic and theoretically grounded choice behavior$-$most notably, substitution patterns. In this work, we propose an amortized inference approach using a neural network emulator to approximate choice probabilities for general error distributions, including those with correlated errors. Our proposal includes a specialized neural network architecture and accompanying training procedures designed to respect the invariance properties of discrete choice models. We provide group-theoretic foundations for the architecture, including a proof of universal approximation given a minimal set of invariant features. Once trained, the emulator enables rapid likelihood evaluation and gradient computation. We use Sobolev training, augmenting the likelihood loss with a gradient-matching penalty so that the emulator learns both choice probabilities and their derivatives. We show that emulator-based maximum likelihood estimators are consistent and asymptotically normal under mild approximation conditions, and we provide sandwich standard errors that remain valid even with imperfect likelihood approximation. Simulations show significant gains over the GHK simulator in accuracy and speed.

Beef Cattle Instance Segmentation Using Fully Convolutional Neural Network

We present an instance segmentation algorithm trained and applied to a CCTV recording of beef cattle during a winter finishing period. A fully convolutional network was transformed into an instance segmentation network that learns to label each instance of an animal separately. We introduce a conceptually simple framework that the network uses to output a single prediction for every animal. These results are a contribution towards behaviour analysis in winter finishing beef cattle for early detection of animal welfare-related problems.