Phase retrieval, the problem of reconstructing a signal from the (squared) magnitude of its Fourier (or any linear) transform, arises in many fields of science and engineering. Such a task is naturally involved in applications such as crystallography (Millane, 1990) and diffraction imaging (Bunk et al., 2007), where optical sensors are able to measure the intensity, but not the phase of a light wave. Due to the loss of phase information, the one-dimensional Fourier phase retrieval problem is ill-posed in general. Common approaches to overcome this ill-posedness include using prior information such as non-negativity, sparsity and the signal's magnitude (Fienup, 1982; Jaganathan et al., 2016), or introducing redundancy into the measurements by oversampling random Gaussian measurements or coded diffraction patterns (Candès et al., 2015; Chen and Candès, 2015). In many applications, the underlying signal is naturally sparse (Jaganathan et al., 2016). A wide range of algorithms has been devised for phase retrieval with a sparse signal, including alternating minimization (SparseAltMinPhase) (Netrapalli et al., 2015), non-convex optimization based approaches such as thresholded Wirtinger flow (TWF) (Cai et al., 2016), sparse truncated amplitude flow (SPARTA) (Wang et al., 2018), compressive reweighted amplitude flow (CRAF) (Zhang et al., 2018) and sparse Wirtinger flow (SWF) (Yuan et al., 2019), and convex relaxation methods such as compressive phase retrieval via lifting (CPRL) (Ohlsson et al., 2012) and SparsePhaseMax (Hand and Voroninski, 2016). Other approaches to sparse phase retrieval include the greedy algorithm GESPAR (Schechtman et al., 2014), an algorithm based on generalized

The recent availability of massive volumes of data fosters the need to design computationally efficient algorithms for optimization in high dimensions. In large-scale machine learning, stochastic gradient descent algorithms are among the most effective optimization methods (Bottou, Curtis and Nocedal 2018). For general smooth convex functions, averaged SGD achieves the rate of convergence of O(1/ k) after k iterations (Nemirovski, Juditsky, Lan and Shapiro 2009). For strongly-convex functions, i.e. when the smallest eigenvalue of the Hessian matrix is bounded away from 0, the convergence rate after k iterations is O(1/k) (Nemirovski, Juditsky, Lan and Shapiro 2009). Variance-reduced SGD algorithms that optimize the sum of n convex functions are described in (Schmidt, Le Roux and Bach 2017, Shalev-Shwartz and Zhang 2013, Johnson and Zhang 2013), and related accelerated methods are analysed in (Shalev-Shwartz and Zhang 2014, Nitanda 2014, Lan and Zhou 2018, Scieur, dAspremont and Bach 2018). These methods enjoy linear convergence(a convergence rate that decreases exponentially with the number of iterations) in the strongly-convex case. For general smooth convex functions, the stochastic average gradient method (SAG) of Schmidt, Le Roux and Bach (2017) yields a convergence rate of O( n/k) after k iterations. This paper focuses on the least-squares regression, which often arises in scientific computing and data analysis, and is widely used for inference and prediction. Many of the modern machine learning techniques such as the logistic and ridge regressions, the lasso method and neural networks can be considered as extensions of the least-squares regression technique.

Learning accurate drug representation is essential for tasks such as computational drug repositioning and prediction of drug side-effects. A drug hierarchy is a valuable source that encodes human knowledge of drug relations in a tree-like structure where drugs that act on the same organs, treat the same disease, or bind to the same biological target are grouped together. However, its utility in learning drug representations has not yet been explored, and currently described drug representations cannot place novel molecules in a drug hierarchy. Here, we develop a semi-supervised drug embedding that incorporates two sources of information: (1) underlying chemical grammar that is inferred from molecular structures of drugs and drug-like molecules (unsupervised), and (2) hierarchical relations that are encoded in an expert-crafted hierarchy of approved drugs (supervised). We use the Variational Auto-Encoder (VAE) framework to encode the chemical structures of molecules and use the knowledge-based drug-drug similarity to induce the clustering of drugs in hyperbolic space. The hyperbolic space is amenable for encoding hierarchical concepts. Both quantitative and qualitative results support that the learned drug embedding can accurately reproduce the chemical structure and induce the hierarchical relations among drugs. Furthermore, our approach can infer the pharmacological properties of novel molecules by retrieving similar drugs from the embedding space. We demonstrate that the learned drug embedding can be used to find new uses for existing drugs and to discover side-effects. We show that it significantly outperforms baselines in both tasks.

We propose a model to tackle classification tasks in the presence of very little training data. To this aim, we approximate the notion of exact match with a theoretically sound mechanism that computes a probability of matching in the input space. Importantly, the model learns to focus on elements of the input that are relevant for the task at hand; by leveraging highlighted portions of the training data, an error boosting technique guides the learning process. In practice, it increases the error associated with relevant parts of the input by a given factor. Remarkable results on text classification tasks confirm the benefits of the proposed approach in both balanced and unbalanced cases, thus being of practical use when labeling new examples is expensive. In addition, by inspecting its weights, it is often possible to gather insights on what the model has learned.

During cluster analysis domain experts and visual analysis are frequently relied on to identify the optimal clustering structure. This process tends to be adhoc, subjective and difficult to reproduce. This work shows how competency questions can be used to formalise expert knowledge and application requirements for context specific evaluation of a clustering application in the residential energy consumption sector. While cluster analysis is an established unsupervised machine learning technique, identifying the optimal set of clusters for a specific application requires extensive experimentation and domain knowledge. Cluster compactness and distinctness are two important attributes that characterise a good cluster set (Sarle et al., 1990) and different metrics, such as the Mean Index Adequacy (MIA), Davies-Bouldin Index (DBI) and the Silhouette Index have been proposed to measure cluster compactness and distinctness.

The `signature method' refers to a collection of feature extraction techniques for multimodal sequential data, derived from the theory of controlled differential equations. Variations exist as many authors have proposed modifications to the method, so as to improve some aspect of it. Here, we introduce a \emph{generalised signature method} that contains these variations as special cases, and groups them conceptually into \emph{augmentations}, \emph{windows}, \emph{transforms}, and \emph{rescalings}. Within this framework we are then able to propose novel variations, and demonstrate how previously distinct options may be combined. We go on to perform an extensive empirical study on 26 datasets as to which aspects of this framework typically produce the best results. Combining the top choices produces a canonical pipeline for the generalised signature method, which demonstrates state-of-the-art accuracy on benchmark problems in multivariate time series classification.

Robustness is a key requirement for widespread deployment of machine learning algorithms, and has received much attention in both statistics and computer science. We study a natural model of robustness for high-dimensional statistical estimation problems that we call the adversarial perturbation model. An adversary can perturb every sample arbitrarily up to a specified magnitude $\delta$ measured in some $\ell_q$ norm, say $\ell_\infty$. Our model is motivated by emerging paradigms such as low precision machine learning and adversarial training. We study the classical problem of estimating the top-$r$ principal subspace of the Gaussian covariance matrix in high dimensions, under the adversarial perturbation model. We design a computationally efficient algorithm that given corrupted data, recovers an estimate of the top-$r$ principal subspace with error that depends on a robustness parameter $\kappa$ that we identify. This parameter corresponds to the $q \to 2$ operator norm of the projector onto the principal subspace, and generalizes well-studied analytic notions of sparsity. Additionally, in the absence of corruptions, our algorithmic guarantees recover existing bounds for problems such as sparse PCA and its higher rank analogs. We also prove that the above dependence on the parameter $\kappa$ is almost optimal asymptotically, not just in a minimax sense, but remarkably for every instance of the problem. This instance-optimal guarantee shows that the $q \to 2$ operator norm of the subspace essentially characterizes the estimation error under adversarial perturbations.

Embedding based models have been the state of the art in collaborative filtering for over a decade. Traditionally, the dot product or higher order equivalents have been used to combine two or more embeddings, e.g., most notably in matrix factorization. In recent years, it was suggested to replace the dot product with a learned similarity e.g. using a multilayer perceptron (MLP). This approach is often referred to as neural collaborative filtering (NCF). In this work, we revisit the experiments of the NCF paper that popularized learned similarities using MLPs. First, we show that with a proper hyperparameter selection, a simple dot product substantially outperforms the proposed learned similarities. Second, while a MLP can in theory approximate any function, we show that it is non-trivial to learn a dot product with an MLP. Finally, we discuss practical issues that arise when applying MLP based similarities and show that MLPs are too costly to use for item recommendation in production environments while dot products allow to apply very efficient retrieval algorithms. We conclude that MLPs should be used with care as embedding combiner and that dot products might be a better default choice.

Network management, whether for malfunction analysis, failure prediction, performance monitoring and improvement, generally involves large amounts of data from different sources. To effectively integrate and manage these sources, automatically finding semantic matches among their schemas or ontologies is crucial. Existing approaches on database matching mainly fall into two categories. One focuses on the schema-level matching based on schema properties such as field names, data types, constraints and schema structures. Network management databases contain massive tables (e.g., network products, incidents, security alert and logs) from different departments and groups with nonuniform field names and schema characteristics. It is not reliable to match them by those schema properties. The other category is based on the instance-level matching using general string similarity techniques, which are not applicable for the matching of large network management databases. In this paper, we develop a matching technique for large NEtwork MAnagement databases (NEMA) deploying instance-level matching for effective data integration and connection. We design matching metrics and scores for both numerical and non-numerical fields and propose algorithms for matching these fields. The effectiveness and efficiency of NEMA are evaluated by conducting experiments based on ground truth field pairs in large network management databases. Our measurement on large databases with 1,458 fields, each of which contains over 10 million records, reveals that the accuracies of NEMA are up to 95%. It achieves 2%-10% higher accuracy and 5x-14x speedup over baseline methods.

Given the problem you want to solve, you will have to investigate and obtain data that you will use to feed your machine. The quality and quantity of information you get are very important since it will directly impact how well or badly your model will work. You may have the information in an existing database or you must create it from scratch. If it is a small project you can create a spreadsheet that will later be easily exported as a CSV file. It is also common to use the web scraping technique to automatically collect information from various sources such as APIs.