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ODTLearn is an open-source Python package that provides methods for learning optimal decision trees for high-stakes predictive and prescriptive tasks based on the mixed-integer optimization (MIO) framework proposed in Aghaei et al. (2019) and several of its extensions. The current version of the package provides implementations for learning optimal classification trees, optimal fair classification trees, optimal classification trees robust to distribution shifts, and optimal prescriptive trees from observational data. We have designed the package to be easy to maintain and extend as new optimal decision tree problem classes, reformulation strategies, and solution algorithms are introduced. To this end, the package follows object-oriented design principles and supports both commercial (Gurobi) and open source (COIN-OR branch and cut) solvers. The package documentation and an extensive user guide can be found at //d3m-research-group.github.io/odtlearn/. Additionally, users can view the package source code and submit feature requests and bug reports by visiting //github.com/D3M-Research-Group/odtlearn.

The ever-growing use of wind energy makes necessary the optimization of turbine operations through pitch angle controllers and their maintenance with early fault detection. It is crucial to have accurate and robust models imitating the behavior of wind turbines, especially to predict the generated power as a function of the wind speed. Existing empirical and physics-based models have limitations in capturing the complex relations between the input variables and the power, aggravated by wind variability. Data-driven methods offer new opportunities to enhance wind turbine modeling of large datasets by improving accuracy and efficiency. In this study, we used physics-informed neural networks to reproduce historical data coming from 4 turbines in a wind farm, while imposing certain physical constraints to the model. The developed models for regression of the power, torque, and power coefficient as output variables showed great accuracy for both real data and physical equations governing the system. Lastly, introducing an efficient evidential layer provided uncertainty estimations of the predictions, proved to be consistent with the absolute error, and made possible the definition of a confidence interval in the power curve.

We establish a connection between stochastic optimal control and generative models based on stochastic differential equations (SDEs), such as recently developed diffusion probabilistic models. In particular, we derive a Hamilton-Jacobi-Bellman equation that governs the evolution of the log-densities of the underlying SDE marginals. This perspective allows to transfer methods from optimal control theory to generative modeling. First, we show that the evidence lower bound is a direct consequence of the well-known verification theorem from control theory. Further, we can formulate diffusion-based generative modeling as a minimization of the Kullback-Leibler divergence between suitable measures in path space. Finally, we develop a novel diffusion-based method for sampling from unnormalized densities -- a problem frequently occurring in statistics and computational sciences. We demonstrate that our time-reversed diffusion sampler (DIS) can outperform other diffusion-based sampling approaches on multiple numerical examples.

Recently, Hegerfeld and Kratsch [ESA 2023] obtained the first tight algorithmic results for hard connectivity problems parameterized by clique-width. Concretely, they gave one-sided error Monte-Carlo algorithms that given a $k$-clique-expression solve Connected Vertex Cover in time $6^kn^{O(1)}$ and Connected Dominating Set in time $5^kn^{O(1)}$. Moreover, under the Strong Exponential-Time Hypothesis (SETH) these results were showed to be tight. However, they leave open several important benchmark problems, whose complexity relative to treewidth had been settled by Cygan et al. [SODA 2011 & TALG 2018]. Among which is the Steiner Tree problem. As a key obstruction they point out the exponential gap between the rank of certain compatibility matrices, which is often used for algorithms, and the largest triangular submatrix therein, which is essential for current lower bound methods. Concretely, for Steiner Tree the $GF(2)$-rank is $4^k$, while no triangular submatrix larger than $3^k$ was known. This yields time $4^kn^{O(1)}$, while the obtainable impossibility of time $(3-\varepsilon)^kn^{O(1)}$ under SETH was already known relative to pathwidth. We close this gap by showing that Steiner Tree can be solved in time $3^kn^{O(1)}$ given a $k$-clique-expression. Hence, for all parameters between cutwidth and clique-width it has the same tight complexity. We first show that there is a ``representative submatrix'' of GF(2)-rank $3^k$ (ruling out larger triangular submatrices). At first glance, this only allows to count (modulo 2) the number of representations of valid solutions, but not the number of solutions (even if a unique solution exists). We show how to overcome this problem by isolating a unique representative of a unique solution, if one exists. We believe that our approach will be instrumental for settling further open problems in this research program.

Few-Shot Learning (FSL) is a challenging task, which aims to recognize novel classes with few examples. Recently, lots of methods have been proposed from the perspective of meta-learning and representation learning. However, few works focus on the interpretability of FSL decision process. In this paper, we take a step towards the interpretable FSL by proposing a novel meta-learning based decision tree framework, namely, MetaDT. In particular, the FSL interpretability is achieved from two aspects, i.e., a concept aspect and a visual aspect. On the concept aspect, we first introduce a tree-like concept hierarchy as FSL prior. Then, resorting to the prior, we split each few-shot task to a set of subtasks with different concept levels and then perform class prediction via a model of decision tree. The advantage of such design is that a sequence of high-level concept decisions that lead up to a final class prediction can be obtained, which clarifies the FSL decision process. On the visual aspect, a set of subtask-specific classifiers with visual attention mechanism is designed to perform decision at each node of the decision tree. As a result, a subtask-specific heatmap visualization can be obtained to achieve the decision interpretability of each tree node. At last, to alleviate the data scarcity issue of FSL, we regard the prior of concept hierarchy as an undirected graph, and then design a graph convolution-based decision tree inference network as our meta-learner to infer parameters of the decision tree. Extensive experiments on performance comparison and interpretability analysis show superiority of our MetaDT.

Trust has emerged as a key factor in people's interactions with AI-infused systems. Yet, little is known about what models of trust have been used and for what systems: robots, virtual characters, smart vehicles, decision aids, or others. Moreover, there is yet no known standard approach to measuring trust in AI. This scoping review maps out the state of affairs on trust in human-AI interaction (HAII) from the perspectives of models, measures, and methods. Findings suggest that trust is an important and multi-faceted topic of study within HAII contexts. However, most work is under-theorized and under-reported, generally not using established trust models and missing details about methods, especially Wizard of Oz. We offer several targets for systematic review work as well as a research agenda for combining the strengths and addressing the weaknesses of the current literature.

The conjoining of dynamical systems and deep learning has become a topic of great interest. In particular, neural differential equations (NDEs) demonstrate that neural networks and differential equation are two sides of the same coin. Traditional parameterised differential equations are a special case. Many popular neural network architectures, such as residual networks and recurrent networks, are discretisations. NDEs are suitable for tackling generative problems, dynamical systems, and time series (particularly in physics, finance, ...) and are thus of interest to both modern machine learning and traditional mathematical modelling. NDEs offer high-capacity function approximation, strong priors on model space, the ability to handle irregular data, memory efficiency, and a wealth of available theory on both sides. This doctoral thesis provides an in-depth survey of the field. Topics include: neural ordinary differential equations (e.g. for hybrid neural/mechanistic modelling of physical systems); neural controlled differential equations (e.g. for learning functions of irregular time series); and neural stochastic differential equations (e.g. to produce generative models capable of representing complex stochastic dynamics, or sampling from complex high-dimensional distributions). Further topics include: numerical methods for NDEs (e.g. reversible differential equations solvers, backpropagation through differential equations, Brownian reconstruction); symbolic regression for dynamical systems (e.g. via regularised evolution); and deep implicit models (e.g. deep equilibrium models, differentiable optimisation). We anticipate this thesis will be of interest to anyone interested in the marriage of deep learning with dynamical systems, and hope it will provide a useful reference for the current state of the art.

In the past few decades, artificial intelligence (AI) technology has experienced swift developments, changing everyone's daily life and profoundly altering the course of human society. The intention of developing AI is to benefit humans, by reducing human labor, bringing everyday convenience to human lives, and promoting social good. However, recent research and AI applications show that AI can cause unintentional harm to humans, such as making unreliable decisions in safety-critical scenarios or undermining fairness by inadvertently discriminating against one group. Thus, trustworthy AI has attracted immense attention recently, which requires careful consideration to avoid the adverse effects that AI may bring to humans, so that humans can fully trust and live in harmony with AI technologies. Recent years have witnessed a tremendous amount of research on trustworthy AI. In this survey, we present a comprehensive survey of trustworthy AI from a computational perspective, to help readers understand the latest technologies for achieving trustworthy AI. Trustworthy AI is a large and complex area, involving various dimensions. In this work, we focus on six of the most crucial dimensions in achieving trustworthy AI: (i) Safety & Robustness, (ii) Non-discrimination & Fairness, (iii) Explainability, (iv) Privacy, (v) Accountability & Auditability, and (vi) Environmental Well-Being. For each dimension, we review the recent related technologies according to a taxonomy and summarize their applications in real-world systems. We also discuss the accordant and conflicting interactions among different dimensions and discuss potential aspects for trustworthy AI to investigate in the future.

Ensembles over neural network weights trained from different random initialization, known as deep ensembles, achieve state-of-the-art accuracy and calibration. The recently introduced batch ensembles provide a drop-in replacement that is more parameter efficient. In this paper, we design ensembles not only over weights, but over hyperparameters to improve the state of the art in both settings. For best performance independent of budget, we propose hyper-deep ensembles, a simple procedure that involves a random search over different hyperparameters, themselves stratified across multiple random initializations. Its strong performance highlights the benefit of combining models with both weight and hyperparameter diversity. We further propose a parameter efficient version, hyper-batch ensembles, which builds on the layer structure of batch ensembles and self-tuning networks. The computational and memory costs of our method are notably lower than typical ensembles. On image classification tasks, with MLP, LeNet, and Wide ResNet 28-10 architectures, our methodology improves upon both deep and batch ensembles.

While deep learning strategies achieve outstanding results in computer vision tasks, one issue remains. The current strategies rely heavily on a huge amount of labeled data. In many real-world problems it is not feasible to create such an amount of labeled training data. Therefore, researchers try to incorporate unlabeled data into the training process to reach equal results with fewer labels. Due to a lot of concurrent research, it is difficult to keep track of recent developments. In this survey we provide an overview of often used techniques and methods in image classification with fewer labels. We compare 21 methods. In our analysis we identify three major trends. 1. State-of-the-art methods are scaleable to real world applications based on their accuracy. 2. The degree of supervision which is needed to achieve comparable results to the usage of all labels is decreasing. 3. All methods share common techniques while only few methods combine these techniques to achieve better performance. Based on all of these three trends we discover future research opportunities.