This complements the list that I posted earlier under the title "Math for Machine Learning: 14 Must-Read Books", available here. Many of the following books have a free PDF version, their own website and GitHub repository, and usually you can purchase the print version. Some are self-published, with the PDF version regularly updated, and even

Controlling the generative model to adapt a new domain with limited samples is a difficult challenge and it is receiving increasing attention. Recently, methods based on meta-learning have shown promising results for few-shot domain adaptation. However, meta-learning-based methods usually suffer from the problem of overfitting, which results in a lack of diversity in the generated texts. To avoid this problem, in this study, a novel framework based on reinforcement learning (RL) is proposed. In this framework, to increase the sample utilization of RL and decrease its sample requirement, maximum likelihood estimation learning is incorporated into the RL process. When there are only a few in-domain samples available, experimental results on five target domains in two few-shot configurations show that this framework performs better than baselines.

Classifying forecasting methods as being either of a "machine learning" or "statistical" nature has become commonplace in parts of the forecasting literature and community, as exemplified by the M4 competition and the conclusion drawn by the organizers. We argue that this distinction does not stem from fundamental differences in the methods assigned to either class. Instead, this distinction is probably of a tribal nature, which limits the insights into the appropriateness and effectiveness of different forecasting methods. We provide alternative characteristics of forecasting methods which, in our view, allow to draw meaningful conclusions. Further, we discuss areas of forecasting which could benefit most from cross-pollination between the ML and the statistics communities.

We propose a path planning methodology for a mobile robot navigating through an obstacle-filled environment to generate a reference path that is traceable with moderate sensing efforts. The desired reference path is characterized as the shortest path in an obstacle-filled Gaussian belief manifold equipped with a novel information-geometric distance function. The distance function we introduce is shown to be an asymmetric quasi-pseudometric and can be interpreted as the minimum information gain required to steer the Gaussian belief. An RRT*-based numerical solution algorithm is presented to solve the formulated shortest-path problem. To gain insight into the asymptotic optimality of the proposed algorithm, we show that the considered path length function is continuous with respect to the topology of total variation. Simulation results demonstrate that the proposed method is effective in various robot navigation scenarios to reduce sensing costs, such as the required frequency of sensor measurements and the number of sensors that must be operated simultaneously.

Label Shift has been widely believed to be harmful to the generalization performance of machine learning models. Researchers have proposed many approaches to mitigate the impact of the label shift, e.g., balancing the training data. However, these methods often consider the underparametrized regime, where the sample size is much larger than the data dimension. The research under the overparametrized regime is very limited. To bridge this gap, we propose a new asymptotic analysis of the Fisher Linear Discriminant classifier for binary classification with label shift. Specifically, we prove that there exists a phase transition phenomenon: Under certain overparametrized regime, the classifier trained using imbalanced data outperforms the counterpart with reduced balanced data. Moreover, we investigate the impact of regularization to the label shift: The aforementioned phase transition vanishes as the regularization becomes strong.

Capturing uncertainty in models of complex dynamical systems is crucial to designing safe controllers. Stochastic noise causes aleatoric uncertainty, whereas imprecise knowledge of model parameters leads to epistemic uncertainty. Several approaches use formal abstractions to synthesize policies that satisfy temporal specifications related to safety and reachability. However, the underlying models exclusively capture aleatoric but not epistemic uncertainty, and thus require that model parameters are known precisely. Our contribution to overcoming this restriction is a novel abstraction-based controller synthesis method for continuous-state models with stochastic noise and uncertain parameters. By sampling techniques and robust analysis, we capture both aleatoric and epistemic uncertainty, with a user-specified confidence level, in the transition probability intervals of a so-called interval Markov decision process (iMDP). We synthesize an optimal policy on this iMDP, which translates (with the specified confidence level) to a feedback controller for the continuous model with the same performance guarantees. Our experimental benchmarks confirm that accounting for epistemic uncertainty leads to controllers that are more robust against variations in parameter values.

In this paper, a hyperparameter tuning based Bayesian optimization of digital twins is carried out to diagnose various faults in grid connected inverters. As fault detection and diagnosis require very high precision, we channelize our efforts towards an online optimization of the digital twins, which, in turn, allows a flexible implementation with limited amount of data. As a result, the proposed framework not only becomes a practical solution for model versioning and deployment of digital twins design with limited data, but also allows integration of deep learning tools to improve the hyperparameter tuning capabilities. For classification performance assessment, we consider different fault cases in virtual synchronous generator (VSG) controlled grid-forming converters and demonstrate the efficacy of our approach. Our research outcomes reveal the increased accuracy and fidelity levels achieved by our digital twin design, overcoming the shortcomings of traditional hyperparameter tuning methods.

From the perspective of machine learning and data science, probabilities and likelihoods are used to quantify uncertainty, or perhaps how probable it is that an observation belongs to one class or another. They crop up when looking at confusion matrices; and indeed, algorithms like Naive Bayes classification are pretty much probabilistic models. The reality is that data scientists cannot escape these concepts. In everyday language, though, we tend to use the terms probability and likelihood almost interchangeably. Indeed, it's not uncommon to hear things like'how likely is it to rain today?' or'what are the chances of this or that happening?'

Bayesian optimization (BO) is a popular paradigm for global optimization of expensive black-box functions, but there are many domains where the function is not completely a black-box. The data may have some known structure (e.g. symmetries) and/or the data generation process may be a composite process that yields useful intermediate or auxiliary information in addition to the value of the optimization objective. However, surrogate models traditionally employed in BO, such as Gaussian Processes (GPs), scale poorly with dataset size and do not easily accommodate known structure. Instead, we use Bayesian neural networks, a class of scalable and flexible surrogate models with inductive biases, to extend BO to complex, structured problems with high dimensionality. We demonstrate BO on a number of realistic problems in physics and chemistry, including topology optimization of photonic crystal materials using convolutional neural networks, and chemical property optimization of molecules using graph neural networks. On these complex tasks, we show that neural networks often outperform GPs as surrogate models for BO in terms of both sampling efficiency and computational cost.

Almost all multi-agent reinforcement learning algorithms without communication follow the principle of centralized training with decentralized execution. During centralized training, agents can be guided by the same signals, such as the global state. During decentralized execution, however, agents lack the shared signal. Inspired by viewpoint invariance and contrastive learning, we propose consensus learning for cooperative multi-agent reinforcement learning in this paper. Although based on local observations, different agents can infer the same consensus in discrete space. During decentralized execution, we feed the inferred consensus as an explicit input to the network of agents, thereby developing their spirit of cooperation. Our proposed method can be extended to various multi-agent reinforcement learning algorithms with small model changes. Moreover, we carry out them on some fully cooperative tasks and get convincing results.