Integrating datasets from different disciplines is hard because the data are often qualitatively different in meaning, scale, and reliability. When two datasets describe the same entities, many scientific questions can be phrased around whether the similarities between entities are conserved. Our method, CLARITY, quantifies consistency across datasets, identifies where inconsistencies arise, and aids in their interpretation. We explore three diverse comparisons: Gene Methylation vs Gene Expression, evolution of language sounds vs word use, and country-level economic metrics vs cultural beliefs. The nonparametric approach is robust to noise and differences in scaling, and makes only weak assumptions about how the data were generated. It operates by decomposing similarities into two components: the'structural' component analogous to a clustering, and an underlying'relationship' between those structures. This allows a'structural comparison' between two similarity matrices using their predictability from'structure'. The software, CLARITY, is available as an R package from github.com/danjlawson/CLARITY.

Rankings are the primary interface through which many online platforms match users to items (e.g. news, products, music, video). In these two-sided markets, not only the users draw utility from the rankings, but the rankings also determine the utility (e.g. exposure, revenue) for the item providers (e.g. publishers, sellers, artists, studios). It has already been noted that myopically optimizing utility to the users, as done by virtually all learning-to-rank algorithms, can be unfair to the item providers. We, therefore, present a learning-to-rank approach for explicitly enforcing merit-based fairness guarantees to groups of items (e.g. articles by the same publisher, tracks by the same artist). In particular, we propose a learning algorithm that ensures notions of amortized group fairness, while simultaneously learning the ranking function from implicit feedback data. The algorithm takes the form of a controller that integrates unbiased estimators for both fairness and utility, dynamically adapting both as more data becomes available. In addition to its rigorous theoretical foundation and convergence guarantees, we find empirically that the algorithm is highly practical and robust.

Every year, criminals launder billions of dollars acquired from serious felonies (e.g., terrorism, drug smuggling, or human trafficking) harming countless people and economies. Cryptocurrencies, in particular, have developed as a haven for money laundering activity. Machine Learning can be used to detect these illicit patterns. However, labels are so scarce that traditional supervised algorithms are inapplicable. Here, we address money laundering detection assuming minimal access to labels. First, we show that existing state-of-the-art solutions using unsupervised anomaly detection methods are inadequate to detect the illicit patterns in a real Bitcoin transaction dataset. Then, we show that our proposed active learning solution is capable of matching the performance of a fully supervised baseline by using just 5\% of the labels. This solution mimics a typical real-life situation in which a limited number of labels can be acquired through manual annotation by experts.

Tensor networks are linear algebraic representations of quantum many-body states based on their entanglement structure. People are exploring their applications to machine learning. Deep convolutional neural networks achieve state of the art results in computer vision and other areas. Supposedly this happens because of parameter sharing, locality, and deepness. We devise a novel tensor network based model called Deep convolutional tensor network (DCTN) for image classification, which has parameter sharing, locality, and deepness. It is based on the Entangled plaquette states (EPS) tensor network. We show how Entangled plaquette states can be implemented as a backpropagatable layer which can be used in neural networks. We test our model on FashionMNIST dataset and find that deepness increases overfitting and decreases test accuracy. Also, we find that the shallow version performs well considering its low parameter count. We discuss how hyperparameters of DCTN affect its training and overfitting.

We propose an adaptation of the Random Forest algorithm to estimate the conditional distribution of a possibly multivariate response. We suggest a new splitting criterion based on the MMD two-sample test, which is suitable for detecting heterogeneity in multivariate distributions. The weights provided by the forest can be conveniently used as an input to other methods in order to locally solve various learning problems. The code is available as \texttt{R}-package \texttt{drf}.

Most applications demand high-performance deep neural architectures costing limited resources. Neural architecture searching is a way of automatically exploring optimal deep neural networks in a given huge search space. However, all sub-networks are usually evaluated using the same criterion; that is, early stopping on a small proportion of the training dataset, which is an inaccurate and highly complex approach. In contrast to conventional methods, here we present a divide-and-conquer (DC) approach to effectively and efficiently search deep neural architectures. Given an arbitrary search space, we first extract feature representations of all sub-networks according to changes in parameters or output features of each layer, and then calculate the similarity between two different sampled networks based on the representations. Then, a k-means clustering is conducted to aggregate similar architectures into the same cluster, separately executing sub-network evaluation in each cluster. The best architecture in each cluster is later merged to obtain the optimal neural architecture. Experimental results conducted on several benchmarks illustrate that DC-NAS can overcome the inaccurate evaluation problem, achieving a $75.1\%$ top-1 accuracy on the ImageNet dataset, which is higher than that of state-of-the-art methods using the same search space.

A random dot product graph (RDPG) is a generative model for networks in which vertices correspond to positions in a latent Euclidean space and edge probabilities are determined by the dot products of the latent positions. We consider RDPGs for which the latent positions are randomly sampled from an unknown $1$-dimensional submanifold of the latent space. In principle, restricted inference, i.e., procedures that exploit the structure of the submanifold, should be more effective than unrestricted inference; however, it is not clear how to conduct restricted inference when the submanifold is unknown. We submit that techniques for manifold learning can be used to learn the unknown submanifold well enough to realize benefit from restricted inference. To illustrate, we test a hypothesis about the Fr\'{e}chet mean of a small community of vertices, using the complete set of vertices to infer latent structure. We propose test statistics that deploy the Isomap procedure for manifold learning, using shortest path distances on neighborhood graphs constructed from estimated latent positions to estimate arc lengths on the unknown $1$-dimensional submanifold. Unlike conventional applications of Isomap, the estimated latent positions do not lie on the submanifold of interest. We extend existing convergence results for Isomap to this setting and use them to demonstrate that, as the number of auxiliary vertices increases, the power of our test converges to the power of the corresponding test when the submanifold is known.

Linear algebra is to machine learning as flour to bakery: every machine learning model is based in linear algebra, as every cake is based in flour. It is not the only ingredient, of course. Machine learning models need vector calculus, probability, and optimization, as cakes need sugar, eggs, and butter. Applied machine learning, like bakery, is essentially about combining these mathematical ingredients in clever ways to create useful (tasty?) models. This document contains introductory level linear algebra notes for applied machine learning. It is meant as a reference rather than a comprehensive review. If you ever get confused by matrix multiplication, don't remember what was the $L_2$ norm, or the conditions for linear independence, this can serve as a quick reference. It also a good introduction for people that don't need a deep understanding of linear algebra, but still want to learn about the fundamentals to read about machine learning or to use pre-packaged machine learning ...

In an ever-increasing interest for Machine Learning (ML) and a favorable data development context, we here propose an original methodology for data-based prediction of two-dimensional physical fields. Polynomial Chaos Expansion (PCE), widely used in the Uncertainty Quantification community (UQ), has recently shown promising prediction characteristics for one-dimensional problems, with advantages that are inherent to the method such as its explicitness and adaptability to small training sets, in addition to the associated probabilistic framework. Simultaneously, Dimensionality Reduction (DR) techniques are increasingly used for pattern recognition and data compression and have gained interest due to improved data quality. In this study, the interest of Proper Orthogonal Decomposition (POD) for the construction of a statistical predictive model is demonstrated. Both POD and PCE have widely proved their worth in their respective frameworks. The goal of the present paper was to combine them for a field-measurement-based forecasting. The described steps are also useful to analyze the data. Some challenging issues encountered when using multidimensional field measurements are addressed, for example when dealing with few data. The POD-PCE coupling methodology is presented, with particular focus on input data characteristics and training-set choice. A simple methodology for evaluating the importance of each physical parameter is proposed for the PCE model and extended to the POD-PCE coupling.

Endowed with higher levels of autonomy, robots are required to perform increasingly complex manipulation tasks. Learning from demonstration is arising as a promising paradigm for transferring skills to robots. It allows to implicitly learn task constraints from observing the motion executed by a human teacher, which can enable adaptive behavior. We present a novel Gaussian-Process-based learning from demonstration approach. This probabilistic representation allows to generalize over multiple demonstrations, and encode variability along the different phases of the task. In this paper, we address how Gaussian Processes can be used to effectively learn a policy from trajectories in task space. We also present a method to efficiently adapt the policy to fulfill new requirements, and to modulate the robot behavior as a function of task variability. This approach is illustrated through a real-world application using the TIAGo robot.