Machine Learning (ML) is one of the most exciting and dynamic areas of modern research and application. The purpose of this review is to provide an introduction to the core concepts and tools of machine learning in a manner easily understood and intuitive to physicists. The review begins by covering fundamental concepts in ML and modern statistics such as the bias-variance tradeoff, overfitting, regularization, and generalization before moving on to more advanced topics in both supervised and unsupervised learning. Topics covered in the review include ensemble models, deep learning and neural networks, clustering and data visualization, energy-based models (including MaxEnt models and Restricted Boltzmann Machines), and variational methods. Throughout, we emphasize the many natural connections between ML and statistical physics. A notable aspect of the review is the use of Python notebooks to introduce modern ML/statistical packages to readers using physics-inspired datasets (the Ising Model and Monte-Carlo simulations of supersymmetric decays of proton-proton collisions). We conclude with an extended outlook discussing possible uses of machine learning for furthering our understanding of the physical world as well as open problems in ML where physicists maybe able to contribute. (Notebooks are available at https://physics.bu.edu/~pankajm/MLnotebooks.html )

In this paper, we investigate the capability of the universal Kriging (UK) model for single-objective global optimization applied within an efficient global optimization (EGO) framework. We implemented this combined UK-EGO framework and studied four variants of the UK methods, that is, a UK with a first-order polynomial, a UK with a second-order polynomial, a blind Kriging (BK) implementation from the ooDACE toolbox, and a polynomial-chaos Kriging (PCK) implementation. The UK-EGO framework with automatic trend function selection derived from the BK and PCK models works by building a UK surrogate model and then performing optimizations via expected improvement criteria on the Kriging model with the lowest leave-one-out cross-validation error. Next, we studied and compared the UK-EGO variants and standard EGO using five synthetic test functions and one aerodynamic problem. Our results show that the proper choice for the trend function through automatic feature selection can improve the optimization performance of UK-EGO relative to EGO. From our results, we found that PCK-EGO was the best variant, as it had more robust performance as compared to the rest of the UK-EGO schemes; however, total-order expansion should be used to generate the candidate trend function set for high-dimensional problems. Note that, for some test functions, the UK with predetermined polynomial trend functions performed better than that of BK and PCK, indicating that the use of automatic trend function selection does not always lead to the best quality solutions. We also found that although some variants of UK are not as globally accurate as the ordinary Kriging (OK), they can still identify better-optimized solutions due to the addition of the trend function, which helps the optimizer locate the global optimum.

The identification of sources of advection-diffusion transport is based usually on solving complex ill-posed inverse models against the available state- variable data records. However, if there are several sources with different locations and strengths, the data records represent mixtures rather than the separate influences of the original sources. Importantly, the number of these original release sources is typically unknown, which hinders reliability of the classical inverse-model analyses. To address this challenge, we present here a novel hybrid method for identification of the unknown number of release sources. Our hybrid method, called HNMF, couples unsupervised learning based on Nonnegative Matrix Factorization (NMF) and inverse-analysis Green functions method. HNMF synergistically performs decomposition of the recorded mixtures, finds the number of the unknown sources and uses the Green function of advection-diffusion equation to identify their characteristics. In the paper, we introduce the method and demonstrate that it is capable of identifying the advection velocity and dispersivity of the medium as well as the unknown number, locations, and properties of various sets of synthetic release sources with different space and time dependencies, based only on the recorded data. HNMF can be applied directly to any problem controlled by a partial-differential parabolic equation where mixtures of an unknown number of sources are measured at multiple locations.

In domains with high knowledge distribution a natural objective is to create principle foundations for collaborative interactive learning environments. We present a first mathematical characterization of a collaborative learning group, a consortium, based on closure systems of attribute sets and the well-known attribute exploration algorithm from formal concept analysis. To this end, we introduce (weak) local experts for subdomains of a given knowledge domain. These entities are able to refute and potentially accept a given (implicational) query for some closure system that is a restriction of the whole domain. On this we build up a consortial expert and show first insights about the ability of such an expert to answer queries. Furthermore, we depict techniques on how to cope with falsely accepted implications and on combining counterexamples. Using notions from combinatorial design theory we further expand those insights as far as providing first results on the decidability problem if a given consortium is able to explore some target domain. Applications in conceptual knowledge acquisition as well as in collaborative interactive ontology learning are at hand.

In this work we study a rational extension $SROEL^R T$ of the low complexity description logic SROEL, which underlies the OWL EL ontology language. The extension involves a typicality operator T, whose semantics is based on Lehmann and Magidor's ranked models and allows for the definition of defeasible inclusions. We consider both rational entailment and minimal entailment. We show that deciding instance checking under minimal entailment is in general $\Pi^P_2$-hard, while, under rational entailment, instance checking can be computed in polynomial time. We develop a Datalog calculus for instance checking under rational entailment and exploit it, with stratified negation, for computing the rational closure of simple KBs in polynomial time.

Successful recurrent models such as long short-term memories (LSTMs) and gated recurrent units (GRUs) use ad hoc gating mechanisms. Empirically these models have been found to improve the learning of medium to long term temporal dependencies and to help with vanishing gradient issues. We prove that learnable gates in a recurrent model formally provide quasi- invariance to general time transformations in the input data. We recover part of the LSTM architecture from a simple axiomatic approach. This result leads to a new way of initializing gate biases in LSTMs and GRUs. Ex- perimentally, this new chrono initialization is shown to greatly improve learning of long term dependencies, with minimal implementation effort.

An important preprocessing step in most data analysis pipelines aims to extract a small set of sources that explain most of the data. Currently used algorithms for blind source separation (BSS), however, often fail to extract the desired sources and need extensive cross-validation. In contrast, their rarely used probabilistic counterparts can get away with little cross-validation and are more accurate and reliable but no simple and scalable implementations are available. Here we present a novel probabilistic BSS framework (DECOMPOSE) that can be flexibly adjusted to the data, is extensible and easy to use, adapts to individual sources and handles large-scale data through algorithmic efficiency. DECOMPOSE encompasses and generalises many traditional BSS algorithms such as PCA, ICA and NMF and we demonstrate substantial improvements in accuracy and robustness on artificial and real data.

When one is faced with a dataset too large to be used all at once, an obvious solution is to retain only part of it. In practice this takes a wide variety of different forms, but among them "coresets" are especially appealing. A coreset is a (small) weighted sample of the original data that comes with a guarantee: that a cost function can be evaluated on the smaller set instead of the larger one, with low relative error. For some classes of problems, and via a careful choice of sampling distribution, iid random sampling has turned to be one of the most successful methods to build coresets efficiently. However, independent samples are sometimes overly redundant, and one could hope that enforcing diversity would lead to better performance. The difficulty lies in proving coreset properties in non-iid samples. We show that the coreset property holds for samples formed with determinantal point processes (DPP). DPPs are interesting because they are a rare example of repulsive point processes with tractable theoretical properties, enabling us to construct general coreset theorems. We apply our results to the $k$-means problem, and give empirical evidence of the superior performance of DPP samples over state of the art methods.

Humans can learn in a continuous manner. Old rarely utilized knowledge can be overwritten by new incoming information while important, frequently used knowledge is prevented from being erased. In artificial learning systems, lifelong learning so far has focused mainly on accumulating knowledge over tasks and overcoming catastrophic forgetting. In this paper, we argue that, given the limited model capacity and the unlimited new information to be learned, knowledge has to be preserved or erased selectively. Inspired by neuroplasticity, we propose a novel approach for lifelong learning, coined Memory Aware Synapses (MAS). It computes the importance of the parameters of a neural network in an unsupervised and online manner. Given a new sample which is fed to the network, MAS accumulates an importance measure for each parameter of the network, based on how sensitive the predicted output function is to a change in this parameter. When learning a new task, changes to important parameters can then be penalized, effectively preventing important knowledge related to previous tasks from being overwritten. Further, we show an interesting connection between a local version of our method and Hebb's rule,which is a model for the learning process in the brain. We test our method on a sequence of object recognition tasks and on the challenging problem of learning an embedding for predicting $<$subject, predicate, object$>$ triplets. We show state-of-the-art performance and, for the first time, the ability to adapt the importance of the parameters based on unlabeled data towards what the network needs (not) to forget, which may vary depending on test conditions.

Proteins are used in various applications by pharmaceutical, food, fuel, and many other industries and their usage is growing steadily (Kirk et al., 2002; Sanchez and Demain, 2010). Proteins have important advantages over chemical catalysts, as they are derived from renewable resources, are biodegradable and are often highly selective (Cherry and Fidantsef, 2003). Protein engineering is used to further improve the properties of proteins, for example to enhance their catalytic activity, modify their substrate specificity or to improve their thermostability (Rapley and Walker, 2000). Increasing the stability is an important aspect of protein engineering, as the proteins used in industry should be stable in the industrial process conditions, which often involve higher than ambient temperature and non-aqueous solvents (Bommarius et al., 2011). The properties of a protein are modified by introducing alterations to its amino acid sequence. Mutations in general tend to be destabilising, and if too many destabilising mutations are implemented, the protein may not remain functional without compensatory stabilising mutations (Tokuriki and Tawfik, 2009). The stability of a protein can be defined as the difference in Gibbs energy G between the folded and unfolded (or native and denaturated) state of the protein.