Unlike classical graphical models, QGMs represent uncertainty with density matrices in complex Hilbert spaces.

Neural Information Processing Systems http://nips.cc/

We compare the performance of human and artificially intelligent (AI) decision makers in simple binary classification tasks where the optimal decision rule is given by Bayes Rule. We reanalyze choices of human subjects gathered from laboratory experiments conducted by El-Gamal and Grether and Holt and Smith. We confirm that while overall, Bayes Rule represents the single best model for predicting human choices, subjects are heterogeneous and a significant share of them make suboptimal choices that reflect judgement biases described by Kahneman and Tversky that include the ``representativeness heuristic'' (excessive weight on the evidence from the sample relative to the prior) and ``conservatism'' (excessive weight on the prior relative to the sample). We compare the performance of AI subjects gathered from recent versions of large language models (LLMs) including several versions of ChatGPT. These general-purpose generative AI chatbots are not specifically trained to do well in narrow decision making tasks, but are trained instead as ``language predictors'' using a large corpus of textual data from the web. We show that ChatGPT is also subject to biases that result in suboptimal decisions. However we document a rapid evolution in the performance of ChatGPT from sub-human performance for early versions (ChatGPT 3.5) to superhuman and nearly perfect Bayesian classifications in the latest versions (ChatGPT 4o).

We consider the problem of binary classification when the covariates conditioned on the each of the response values follow multivariate Gaussian distributions. We focus on the setting where the covariance matrices for the two conditional distributions are the same. The corresponding generative model classifier, derived via the Bayes rule, also called Linear Discriminant Analysis, has been shown to behave poorly in high-dimensional settings. We present a novel analysis of the classification error of any linear discriminant approach given conditional Gaussian models. This allows us to compare the generative model classifier, other recently proposed discriminative approaches that directly learn the discriminant function, and then finally logistic regression which is another classical discriminative model classifier.

Semi-supervised learning (SSL) approaches have been successfully applied in a wide range of engineering and scientific fields. This paper investigates the generative model framework with a missingness mechanism for unclassified observations, as introduced by Ahfock and McLachlan(2020). We show that in a partially classified sample, a classifier using Bayes rule of allocation with a missing-data mechanism can surpass a fully supervised classifier in a two-class normal homoscedastic model, especially with moderate to low overlap and proportion of missing class labels, or with large overlap but few missing labels. It also outperforms a classifier with no missing-data mechanism regardless of the overlap region or the proportion of missing class labels. Our exploration of two- and three-component normal mixture models with unequal covariances through simulations further corroborates our findings. Finally, we illustrate the use of the proposed classifier with a missing-data mechanism on interneuronal and skin lesion datasets.

Reinforcement learning-based large language models, such as ChatGPT, are believed to have potential to aid human experts in many domains, including healthcare. There is, however, little work on ChatGPT's ability to perform a key task in healthcare: formal, probabilistic medical diagnostic reasoning. This type of reasoning is used, for example, to update a pre-test probability to a post-test probability. In this work, we probe ChatGPT's ability to perform this task. In particular, we ask ChatGPT to give examples of how to use Bayes rule for medical diagnosis. Our prompts range from queries that use terminology from pure probability (e.g., requests for a posterior of A given B and C) to queries that use terminology from medical diagnosis (e.g., requests for a posterior probability of Covid given a test result and cough). We show how the introduction of medical variable names leads to an increase in the number of errors that ChatGPT makes. Given our results, we also show how one can use prompt engineering to facilitate ChatGPT's partial avoidance of these errors. We discuss our results in light of recent commentaries on sensitivity and specificity. We also discuss how our results might inform new research directions for large language models.

Segmentation has emerged as a fundamental field of computer vision and natural language processing, which assigns a label to every pixel/feature to extract regions of interest from an image/text. To evaluate the performance of segmentation, the Dice and IoU metrics are used to measure the degree of overlap between the ground truth and the predicted segmentation. In this paper, we establish a theoretical foundation of segmentation with respect to the Dice/IoU metrics, including the Bayes rule and Dice-/IoU-calibration, analogous to classification-calibration or Fisher consistency in classification. We prove that the existing thresholding-based framework with most operating losses are not consistent with respect to the Dice/IoU metrics, and thus may lead to a suboptimal solution. To address this pitfall, we propose a novel consistent ranking-based framework, namely RankDice/RankIoU, inspired by plug-in rules of the Bayes segmentation rule. Three numerical algorithms with GPU parallel execution are developed to implement the proposed framework in large-scale and high-dimensional segmentation. We study statistical properties of the proposed framework. We show it is Dice-/IoU-calibrated, and its excess risk bounds and the rate of convergence are also provided. The numerical effectiveness of RankDice/mRankDice is demonstrated in various simulated examples and Fine-annotated CityScapes, Pascal VOC and Kvasir-SEG datasets with state-of-the-art deep learning architectures.

Spike trains data find a growing list of applications in computational neuroscience, imaging, streaming data and finance. Machine learning strategies for spike trains are based on various neural network and probabilistic models. The probabilistic approach is relying on parametric or nonparametric specifications of the underlying spike generation model. In this paper we consider the two-class statistical classification problem for a class of spike train data characterized by nonparametrically specified intensity functions. We derive the optimal Bayes rule and next form the plug-in nonparametric kernel classifier. Asymptotical properties of the rules are established including the limit with respect to the increasing recording time interval and the size of a training set. In particular the convergence of the kernel classifier to the Bayes rule is proved. The obtained results are supported by a finite sample simulation studies.

The classical Bayes rule computes the posterior model probability from the prior probability and the data likelihood. We generalize this rule to the case when the prior is a density matrix (symmetric positive definite and trace one) and the data likelihood a covariance matrix. The classical Bayes rule is retained as the special case when the matrices are diagonal. In the classical setting, the calculation of the probability of the data is an expected likelihood, where the expectation is over the prior distribution. In the generalized setting, this is replaced by an expected variance calculation where the variance is computed along the eigenvectors of the prior density matrix and the expectation is over the eigenvalues of the density matrix (which form a probability vector).

We mimic the cognitive ability of Human perception, based on Bayesian hypothesis, to recognize view-based 3D objects. We consider approximate Bayesian (Empirical Bayesian) for perceptual inference for recognition. We essentially handle computation with perception.