Tree-based models such as decision trees and random forests (RF) are a cornerstone of modern machine-learning practice. To mitigate overfitting, trees are typically regularized by a variety of techniques that modify their structure (e.g. pruning). We introduce Hierarchical Shrinkage (HS), a post-hoc algorithm that does not modify the tree structure, and instead regularizes the tree by shrinking the prediction over each node towards the sample means of its ancestors. The amount of shrinkage is controlled by a single regularization parameter and the number of data points in each ancestor. Since HS is a post-hoc method, it is extremely fast, compatible with any tree growing algorithm, and can be used synergistically with other regularization techniques. Extensive experiments over a wide variety of real-world datasets show that HS substantially increases the predictive performance of decision trees, even when used in conjunction with other regularization techniques. Moreover, we find that applying HS to each tree in an RF often improves accuracy, as well as its interpretability by simplifying and stabilizing its decision boundaries and SHAP values. We further explain the success of HS in improving prediction performance by showing its equivalence to ridge regression on a (supervised) basis constructed of decision stumps associated with the internal nodes of a tree. All code and models are released in a full-fledged package available on Github (github.com/csinva/imodels)

Representing words by vectors, or embeddings, enables computational reasoning and is foundational to automating natural language tasks. For example, if word embeddings of similar words contain similar values, word similarity can be readily assessed, whereas judging that from their spelling is often impossible (e.g. cat /feline) and to predetermine and store similarities between all words is prohibitively time-consuming, memory intensive and subjective. We focus on word embeddings learned from text corpora and knowledge graphs. Several well-known algorithms learn word embeddings from text on an unsupervised basis by learning to predict those words that occur around each word, e.g. word2vec and GloVe. Parameters of such word embeddings are known to reflect word co-occurrence statistics, but how they capture semantic meaning has been unclear. Knowledge graph representation models learn representations both of entities (words, people, places, etc.) and relations between them, typically by training a model to predict known facts in a supervised manner. Despite steady improvements in fact prediction accuracy, little is understood of the latent structure that enables this. The limited understanding of how latent semantic structure is encoded in the geometry of word embeddings and knowledge graph representations makes a principled means of improving their performance, reliability or interpretability unclear. To address this: 1. we theoretically justify the empirical observation that particular geometric relationships between word embeddings learned by algorithms such as word2vec and GloVe correspond to semantic relations between words; and 2. we extend this correspondence between semantics and geometry to the entities and relations of knowledge graphs, providing a model for the latent structure of knowledge graph representation linked to that of word embeddings.

Despite the non-convex optimization landscape, over-parametrized shallow networks are able to achieve global convergence under gradient descent. The picture can be radically different for narrow networks, which tend to get stuck in badly-generalizing local minima. Here we investigate the cross-over between these two regimes in the high-dimensional setting, and in particular investigate the connection between the so-called mean-field/hydrodynamic regime and the seminal approach of Saad & Solla. Focusing on the case of Gaussian data, we study the interplay between the learning rate, the time scale, and the number of hidden units in the high-dimensional dynamics of stochastic gradient descent (SGD). Our work builds on a deterministic description of SGD in high-dimensions from statistical physics, which we extend and for which we provide rigorous convergence rates.

Earth could have as many as 73,000 tree species, a new first-of-its-kind study has estimated, including some 9,200 that are yet to be discovered. Most of these undiscovered species are likely to be rare, in very low numbers and at threat from human-driven changes in land use and climate, researchers said. South America contains about 43 per cent of the world's tree species and the highest number of rare ones. The findings suggest the continent should be the focus of conservation efforts, along with global tropical and subtropical forests, which also likely harbour many rare, undiscovered species, according to researchers. The study is the outcome of a three-year international project that involved almost 150 scientists and led to the identification of approximately 40 million trees belonging to 64,000 species.

In industries from healthcare to education to finance to manufacturing, quarantine and extended work-from-home forced companies to use technology to reimagine nearly every facet of their operations. As the world reopens in fits and starts, we analyze the industries poised to thrive in a post-Covid world. As the Covid-19 pandemic has charted its unprecedented path around the world, it's carried with it the question: What will Covid-19's legacy be? From healthcare to education to entertainment to manufacturing, technology innovators are stepping forward to help answer that question. "Crisis can be… a catalyst or can speed up changes that are on the way -- it almost can serve as an accelerant." In the wake of the outbreak, everything from doctors appointments to schooling to workouts went online. As more people have worked, learned, banked, exercised, relaxed, and even sought medical care from home during Covid-19, they have gotten a crash course in just how much can be accomplished at ...

A 2019 study conducted by DataChildFutures found that 46% of participating Italian households had AI-powered speakers, while 40% of toys were connected to the internet. More recent research suggests that by 2023 more than 275 million intelligent voice assistants, such as Amazon Echo or Google Home, will be installed in homes worldwide. As younger generations grow up interacting with AI-enabled devices, more consideration should be given to the impact of this technology on children, their rights and wellbeing. AI-powered learning tools and approaches are often regarded as critical drivers of innovation in the education sector. Often recognized for its ability to improve the quality of learning and teaching, artificial intelligence is being used to monitor students' level of knowledge and learning habits, such as rereading and task prioritization, and ultimately to provide a personalized approach to learning. Knewton is one example of AI-enabled learning software that identifies knowledge gaps and curates education content in line with user needs.

Encoding facts as representations of entities and binary relationships between them, as learned by knowledge graph representation models, is useful for various tasks, including predicting new facts, question answering, fact checking and information retrieval. The focus of this thesis is on (i) improving knowledge graph representation with the aim of tackling the link prediction task; and (ii) devising a theory on how semantics can be captured in the geometry of relation representations. Most knowledge graphs are very incomplete and manually adding new information is costly, which drives the development of methods which can automatically infer missing facts. The first contribution of this thesis is HypER, a convolutional model which simplifies and improves upon the link prediction performance of the existing convolutional state-of-the-art model ConvE and can be mathematically explained in terms of constrained tensor factorisation. The second contribution is TuckER, a relatively straightforward linear model, which, at the time of its introduction, obtained state-of-the-art link prediction performance across standard datasets. The third contribution is MuRP, first multi-relational graph representation model embedded in hyperbolic space. MuRP outperforms all existing models and its Euclidean counterpart MuRE in link prediction on hierarchical knowledge graph relations whilst requiring far fewer dimensions. Despite the development of a large number of knowledge graph representation models with gradually increasing predictive performance, relatively little is known of the latent structure they learn. We generalise recent theoretical understanding of how semantic relations of similarity, paraphrase and analogy are encoded in the geometric interactions of word embeddings to how more general relations, as found in knowledge graphs, can be encoded in their representations.

In this manuscript, we offer a gentle review of submodularity and supermodularity and their properties. We offer a plethora of submodular definitions; a full description of a number of example submodular functions and their generalizations; example discrete constraints; a discussion of basic algorithms for maximization, minimization, and other operations; a brief overview of continuous submodular extensions; and some historical applications. We then turn to how submodularity is useful in machine learning and artificial intelligence. This includes summarization, and we offer a complete account of the differences between and commonalities amongst sketching, coresets, extractive and abstractive summarization in NLP, data distillation and condensation, and data subset selection and feature selection. We discuss a variety of ways to produce a submodular function useful for machine learning, including heuristic hand-crafting, learning or approximately learning a submodular function or aspects thereof, and some advantages of the use of a submodular function as a coreset producer. We discuss submodular combinatorial information functions, and how submodularity is useful for clustering, data partitioning, parallel machine learning, active and semi-supervised learning, probabilistic modeling, and structured norms and loss functions.

AlphaGo, AlphaGo Zero, and all of their derivatives can play with superhuman strength because they are able to predict the win-lose outcome with great accuracy. However, Go as a game is decided by a final score difference, and in final positions AlphaGo plays suboptimal moves: this is not surprising, since AlphaGo is completely unaware of the final score difference, all winning final positions being equivalent from the winrate perspective. This can be an issue, for instance when trying to learn the "best" move or to play with an initial handicap. Moreover, there is the theoretical quest of the "perfect game", that is, the minimax solution. Thus, a natural question arises: is it possible to train a successful Reinforcement Learning agent to predict score differences instead of winrates? No empirical or theoretical evidence can be found in the literature to support the folklore statement that "this does not work". In this paper we present Leela Zero Score, a software designed to support or disprove the "does not work" statement. Leela Zero Score is designed on the open-source solution known as Leela Zero, and is trained on a 9x9 board to predict score differences instead of winrates. We find that the training produces a rational player, and we analyze its style against a strong amateur human player, to find that it is prone to some mistakes when the outcome is close. We compare its strength against SAI, an AlphaGo Zero-like software working on the 9x9 board, and find that the training of Leela Zero Score has reached a premature convergence to a player weaker than SAI.

Kernel mean embeddings are a powerful tool to represent probability distributions over arbitrary spaces as single points in a Hilbert space. Yet, the cost of computing and storing such embeddings prohibits their direct use in large-scale settings. We propose an efficient approximation procedure based on the Nystr\"om method, which exploits a small random subset of the dataset. Our main result is an upper bound on the approximation error of this procedure. It yields sufficient conditions on the subsample size to obtain the standard $n^{-1/2}$ rate while reducing computational costs. We discuss applications of this result for the approximation of the maximum mean discrepancy and quadrature rules, and illustrate our theoretical findings with numerical experiments.