We introduce automated scientific minimization of regret (ASMR) -- a framework for automated computational cognitive science. Building on the principles of scientific regret minimization, ASMR leverages Centaur -- a recently proposed foundation model of human cognition -- to identify gaps in an interpretable cognitive model. These gaps are then addressed through automated revisions generated by a language-based reasoning model. We demonstrate the utility of this approach in a multi-attribute decision-making task, showing that ASMR discovers cognitive models that predict human behavior at noise ceiling while retaining interpretability. Taken together, our results highlight the potential of ASMR to automate core components of the cognitive modeling pipeline.

This study explores the computational mechanisms underlying the resolution of cognitive dissonances. We focus on scenarios in which an observation violates the expected relationship between objects. For instance, an agent expects object A to be smaller than B in some feature space but observes the opposite. One solution is to adjust the expected relationship according to the new observation and change the expectation to A being larger than B. An alternative solution would be to adapt the representation of A and B in the feature space such that in the new representation, the relationship that A is smaller than B is maintained. While both pathways resolve the dissonance, they generalize differently to different tasks. Using Artificial Neural Networks (ANNs) capable of relational learning, we demonstrate the existence of these two pathways and show that the chosen pathway depends on the dissonance magnitude. Large dissonances alter the representation of the objects, while small dissonances lead to adjustments in the expected relationships. We show that this effect arises from the inherently different learning dynamics of relationships and representations and study the implications.

The Gradient Boosting Classifier (GBC) is a widely used machine learning algorithm for binary classification, which builds decision trees iteratively to minimize prediction errors. This document explains the GBC's training and prediction processes, focusing on the computation of terminal node values $\gamma_j$, which are crucial to optimizing the logistic loss function. We derive $\gamma_j$ through a Taylor series approximation and provide a step-by-step pseudocode for the algorithm's implementation. The guide explains the theory of GBC and its practical application, demonstrating its effectiveness in binary classification tasks. We provide a step-by-step example in the appendix to help readers understand.

Multiple Instance Learning (MIL) is a weakly supervised paradigm that has been successfully applied to many different scientific areas and is particularly well suited to medical imaging. Probabilistic MIL methods, and more specifically Gaussian Processes (GPs), have achieved excellent results due to their high expressiveness and uncertainty quantification capabilities. One of the most successful GP-based MIL methods, VGPMIL, resorts to a variational bound to handle the intractability of the logistic function. Here, we formulate VGPMIL using P\'olya-Gamma random variables. This approach yields the same variational posterior approximations as the original VGPMIL, which is a consequence of the two representations that the Hyperbolic Secant distribution admits. This leads us to propose a general GP-based MIL method that takes different forms by simply leveraging distributions other than the Hyperbolic Secant one. Using the Gamma distribution we arrive at a new approach that obtains competitive or superior predictive performance and efficiency. This is validated in a comprehensive experimental study including one synthetic MIL dataset, two well-known MIL benchmarks, and a real-world medical problem. We expect that this work provides useful ideas beyond MIL that can foster further research in the field.

Information borrowing from historical data is gaining attention in clinical trials of rare and pediatric diseases, where statistical power may be insufficient for confirmation of efficacy if the sample size is small. Although Bayesian information borrowing methods are well established, test-then-pool and equivalence-based test-then-pool methods have recently been proposed as frequentist methods to determine whether historical data should be used for statistical hypothesis testing. Depending on the results of the hypothesis testing, historical data may not be usable. This paper proposes a dynamic borrowing method for historical information based on the similarity between current and historical data. In our proposed method of dynamic information borrowing, as in Bayesian dynamic borrowing, the amount of borrowing ranges from 0% to 100%. We propose two methods using the density function of the t-distribution and a logistic function as a similarity measure. We evaluate the performance of the proposed methods through Monte Carlo simulations. We demonstrate the usefulness of borrowing information by reanalyzing actual clinical trial data.

XGBoost, LightGBM, or CatBoost are libraries that share (by default) the same kind of underlying model: decision trees. These decision trees are combined iteratively, using Gradient Boosting. I.e. the addition of new nodes to the current tree is done so that a non-linear objective, usually the squared error, is optimized. To handle the non-linearity, the objective is linearized using its Gradient and Hessian. As a reminder, the prediction process is relatively simple: given a row of data, each decision tree of the ensemble is browsed.

This work builds on the models and concepts presented in part 1 to learn approximate dictionary representations of Koopman operators from data. Part I of this paper presented a methodology for arguing the subspace invariance of a Koopman dictionary. This methodology was demonstrated on the state-inclusive logistic lifting (SILL) basis. This is an affine basis augmented with conjunctive logistic functions. The SILL dictionary's nonlinear functions are homogeneous, a norm in data-driven dictionary learning of Koopman operators. In this paper, we discover that structured mixing of heterogeneous dictionary functions drawn from different classes of nonlinear functions achieve the same accuracy and dimensional scaling as the deep-learning-based deepDMD algorithm. We specifically show this by building a heterogeneous dictionary comprised of SILL functions and conjunctive radial basis functions (RBFs). This mixed dictionary achieves the same accuracy and dimensional scaling as deepDMD with an order of magnitude reduction in parameters, while maintaining geometric interpretability. These results strengthen the viability of dictionary-based Koopman models to solving high-dimensional nonlinear learning problems.

This nonstandard state is often called a Koopman observable and is usually approximated numerically by a superposition of functions drawn from a dictionary. In a widely used algorithm, Extended Dynamic Mode Decomposition, the dictionary functions are drawn from a fixed class of functions. Recently, deep learning combined with EDMD has been used to learn novel dictionary functions in an algorithm called deep dynamic mode decomposition (deepDMD). The learned representation both (1) accurately models and (2) scales well with the dimension of the original nonlinear system. In this paper we analyze the learned dictionaries from deepDMD and explore the theoretical basis for their strong performance. We explore State-Inclusive Logistic Lifting (SILL) dictionary functions to approximate Koopman observables. Error analysis of these dictionary functions show they satisfy a property of subspace approximation, which we define as uniform finite approximate closure. Our results provide a hypothesis to explain the success of deep neural networks in learning numerical approximations to Koopman operators. Part 2 of this paper, [10], will extend this explanation by demonstrating the subspace invariant of heterogeneous dictionaries and presenting a head-to-head numerical comparison of deepDMD and low-parameter heterogeneous dictionary learning.

Logistic regression is a method to create a model by using binary data (0 and 1). The goal is to predict something independent variable based on a dependent variable. In a real application, logistic regression is applied to predict the number of customers who buy a product or who did not base on their previous transaction, to predict the number of fraud transactions in credit cards, and so on. In logistic regression, Y-axis lies from 0 – 1. Logistic regression cannot be solved by using a linear equation like linear regression. That is because if the Y-axis of the logistic function is transformed into a linear function, the boundary of the Y-axis lies from -infinity to infinity. Then, when we calculate the misfit error between actual data and predicted data, it will not get a good misfit error.