This primer is an attempt to provide a detailed summary of the different facets of lifelong learning. We start with Chapter 2 which provides a high-level overview of lifelong learning systems. In this chapter, we discuss prominent scenarios in lifelong learning (Section 2.4), provide 8 Introduction a high-level organization of different lifelong learning approaches (Section 2.5), enumerate the desiderata for an ideal lifelong learning system (Section 2.6), discuss how lifelong learning is related to other learning paradigms (Section 2.7), describe common metrics used to evaluate lifelong learning systems (Section 2.8). This chapter is more useful for readers who are new to lifelong learning and want to get introduced to the field without focusing on specific approaches or benchmarks. The remaining chapters focus on specific aspects (either learning algorithms or benchmarks) and are more useful for readers who are looking for specific approaches or benchmarks. Chapter 3 focuses on regularization-based approaches that do not assume access to any data from previous tasks. Chapter 4 discusses memory-based approaches that typically use a replay buffer or an episodic memory to save subset of data across different tasks. Chapter 5 focuses on different architecture families (and their instantiations) that have been proposed for training lifelong learning systems. Following these different classes of learning algorithms, we discuss the commonly used evaluation benchmarks and metrics for lifelong learning (Chapter 6) and wrap up with a discussion of future challenges and important research directions in Chapter 7.

Consider the finite state graph that results from a simple, discrete, dynamical system in which an agent moves in a rectangular grid picking up and dropping packages. Can the state variables of the problem, namely, the agent location and the package locations, be recovered from the structure of the state graph alone without having access to information about the objects, the structure of the states, or any background knowledge? We show that this is possible provided that the dynamics is learned over a suitable domain-independent first-order causal language that makes room for objects and relations that are not assumed to be known. The preference for the most compact representation in the language that is compatible with the data provides a strong and meaningful learning bias that makes this possible. The language of structured causal models (SCMs) is the standard language for representing (static) causal models but in dynamic worlds populated by objects, first-order causal languages such as those used in "classical AI planning" are required. While "classical AI" requires handcrafted representations, similar representations can be learned from unstructured data over the same languages. Indeed, it is the languages and the preference for compact representations in those languages that provide structure to the world, uncovering objects, relations, and causes.

We develop a multiscale approach to estimate high-dimensional probability distributions from a dataset of physical fields or configurations observed in experiments or simulations. In this way we can estimate energy functions (or Hamiltonians) and efficiently generate new samples of many-body systems in various domains, from statistical physics to cosmology. Our method -- the Wavelet Conditional Renormalization Group (WC-RG) -- proceeds scale by scale, estimating models for the conditional probabilities of "fast degrees of freedom" conditioned by coarse-grained fields. These probability distributions are modeled by energy functions associated with scale interactions, and are represented in an orthogonal wavelet basis. WC-RG decomposes the microscopic energy function as a sum of interaction energies at all scales and can efficiently generate new samples by going from coarse to fine scales. Near phase transitions, it avoids the "critical slowing down" of direct estimation and sampling algorithms. This is explained theoretically by combining results from RG and wavelet theories, and verified numerically for the Gaussian and $\varphi^4$ field theories. We show that multiscale WC-RG energy-based models are more general than local potential models and can capture the physics of complex many-body interacting systems at all length scales. This is demonstrated for weak-gravitational-lensing fields reflecting dark matter distributions in cosmology, which include long-range interactions with long-tail probability distributions. WC-RG has a large number of potential applications in non-equilibrium systems, where the underlying distribution is not known {\it a priori}. Finally, we discuss the connection between WC-RG and deep network architectures.

Despite the progress observed with model-agnostic explainable AI (XAI), it is the case that model-agnostic XAI can produce incorrect explanations. One alternative are the so-called formal approaches to XAI, that include PI-explanations. Unfortunately, PI-explanations also exhibit important drawbacks, the most visible of which is arguably their size. The computation of relevant features serves to trade off probabilistic precision for the number of features in an explanation. However, even for very simple classifiers, the complexity of computing sets of relevant features is prohibitive. This paper investigates the computation of relevant sets for Naive Bayes Classifiers (NBCs), and shows that, in practice, these are easy to compute. Furthermore, the experiments confirm that succinct sets of relevant features can be obtained with NBCs.

We study the problem of learning the structure of an optimal Bayesian network when additional constraints are posed on the network or on its moralized graph. More precisely, we consider the constraint that the network or its moralized graph are close, in terms of vertex or edge deletions, to a sparse graph class Π. For example, we show that learning an optimal network whose moralized graph has vertex deletion distance at most k from a graph with maximum degree 1 can be computed in polynomial time when k is constant. This extends previous work that gave an algorithm with such a running time for the vertex deletion distance to edgeless graphs. We then show that further extensions or improvements are presumably impossible. For example, we show that learning optimal networks where the network or its moralized graph have maximum degree 2 or connected components of size at most c, c ≥ 3, is NP-hard. Finally, we show that learning an optimal network with at most k edges in the moralized graph presumably has no f(k) · |I|O(1)-time algorithm and that, in contrast, an optimal network with at most k arcs can be computed in 2O(k) · |I|O(1) time where |I| is the total input size.

The book covers a broad array of topics not usually included in introductory machine learning texts, including supervised learning, Bayesian decision theory, parametric methods, semiparametric methods, nonparametric methods, multivariate analysis, hidden Markov models, reinforcement learning, kernel machines, graphical models, Bayesian estimation, and statistical testing. The fourth edition offers a new chapter on deep learning that discusses training, regularizing, and structuring deep neural networks such as convolutional and generative adversarial networks; new material in the chapter on reinforcement learning that covers the use of deep networks, the policy gradient methods, and deep reinforcement learning; new material in the chapter on multilayer perceptrons on autoencoders and the word2vec network; and discussion of a popular method of dimensionality reduction, t-SNE. New appendixes offer background material on linear algebra and optimization. End-of-chapter exercises help readers to apply concepts learned. Introduction to Machine Learning can be used in courses for advanced undergraduate and graduate students and as a reference for professionals.

How to sample high quality negative instances from unlabeled data, i.e., negative sampling, is important for training implicit collaborative filtering and contrastive learning models. Although previous studies have proposed some approaches to sample informative instances, few has been done to discriminating false negative from true negative for unbiased negative sampling. On the basis of our order relation analysis of negatives' scores, we first derive the class conditional density of true negatives and that of false negatives. We next design a Bayesian classifier for negative classification, from which we define a model-agnostic posterior probability estimate of an instance being true negative as a quantitative negative signal measure. We also propose a Bayesian optimal sampling rule to sample high-quality negatives. The proposed Bayesian Negative Sampling (BNS) algorithm has a linear time complexity. Experimental studies validate the superiority of BNS over the peers in terms of better sampling quality and better recommendation performance.

A major issue in the association of genes to neuroimaging phenotypes is the high dimension of both genetic data and neuroimaging data. In this article, we tackle the latter problem with an eye toward developing solutions that are relevant for disease prediction. Supported by a vast literature on the predictive power of neural networks, our proposed solution uses neural networks to extract from neuroimaging data features that are relevant for predicting Alzheimer's Disease (AD) for subsequent relation to genetics. Our neuroimaging-genetic pipeline is comprised of image processing, neuroimaging feature extraction and genetic association steps. We propose a neural network classifier for extracting neuroimaging features that are related with disease and a multivariate Bayesian group sparse regression model for genetic association. We compare the predictive power of these features to expert selected features and take a closer look at the SNPs identified with the new neuroimaging features.

Bayesian hierarchical models are well-suited to analyzing the often noisy data from electroencephalography experiments in cognitive neuroscience: these models provide an intuitive framework to account for structures and correlations in the data, and they allow a straightforward handling of uncertainty. In a typical neurolinguistic experiment, event-related potentials show only very small effect sizes and frequentist approaches to data analysis fail to establish the significance of some of these effects. Here, we present a Bayesian approach to analyzing event-related potentials using as an example data from an experiment which relates word surprisal and neural response. Our model is able to estimate the effect of word surprisal on most components of the event-related potential and provides a richer description of the data. The Bayesian framework also allows easier comparison between estimates based on surprisal values calculated using different language models.

Unlike linear models and SVM (see Part 1), some machine learning models are really complex to learn from their mathematical formulation. Fortunately, they can be understood by following a step-by-step process they execute on a small dummy dataset. This way, you can uncover machine learning models under the hood without the "math bottleneck". You will learn three more models in this story after Part 1: K-Nearest Neighbors (KNN), Naive Bayes, and Decision Tree. KNN is a non-generalizing machine learning model since it simply "remembers" all of its train data.