There are already a fair number of books about Numpy (see Bibliography) and a legitimate question is to wonder if another book is really necessary. As you may have guessed by reading these lines, my personal answer is yes, mostly because I think there is room for a different approach concentrating on the migration from Python to Numpy through vectorization. There are a lot of techniques that you don't find in books and such techniques are mostly learned through experience. The goal of this book is to explain some of these techniques and to provide an opportunity for making this experience in the process. Disclaimer: All external pictures should have associated credits.

Incremental versions of batch algorithms are often desired, for increased time efficiency in the streaming data setting, or increased memory efficiency in general. In this paper we present a novel algorithm for incremental kernel PCA, based on rank one updates to the eigendecomposition of the kernel matrix, which is more computationally efficient than comparable existing algorithms. We extend our algorithm to incremental calculation of the Nystr\"om approximation to the kernel matrix, the first such algorithm proposed. Incremental calculation of the Nystr\"om approximation leads to further gains in memory efficiency, and allows for empirical evaluation of when a subset of sufficient size has been obtained.

The extent to which individuals experience positive and negative affect on a daily basis is associated with mental health outcomes [1]. Higher levels of negative affect are associated with increased vulnerability to many mental disorders, including depression and anxiety disorders, two of the most common types of mental disorders in U.S. adults [2]. Mental health research typically relies on self-report questionnaires that assess negative affect at a moment in time. Repeated administration of these measures, such as in an ecological momentary assessment (EMA) framework, is resource intensive and susceptible to retrospective bias when participants are asked to recall their mood over a previous duration [3]. Ideally, negative affect would be recognized without asking participants, thereby reducing burden, improving compliance among participants, and allowing for continuous modeling of affect change.

Gaussian process (GP) models provide a powerful tool for prediction but are computationally prohibitive using large data sets. In such scenarios, one has to resort to approximate methods. We derive an approximation based on a composite likelihood approach using a general belief updating framework, which leads to a recursive computation of the predictor as well as of learning the hyper-parameters. We then provide an analysis of the derived composite GP model in predictive and information-theoretic terms. Finally, we evaluate the approximation with both synthetic data and a real-world application.

--We study the problem of learning to rank from multiple sources. Though multi-view learning and learning to rank have been studied extensively leading to a wide range of applications, multi-view learning to rank as a synergy of both topics has received little attention. The aim of the paper is to propose a composite ranking method while keeping a close correlation with the individual rankings simultaneously . We propose a multi-objective solution to ranking by capturing the information of the feature mapping from both within each view as well as across views using autoencoder-like networks. Moreover, a novel end-to-end solution is introduced to enhance the joint ranking with minimum view-specific ranking loss, so that we can achieve the maximum global view agreements within a single optimization process. The proposed method is validated on a wide variety of ranking problems, including university ranking, multi-view lingual text ranking and image data ranking, providing superior results. Learning to rank is an important research topic in information retrieval and data mining, which aims to learn a ranking model to produce a query-specfic ranking list. The ranking model establishes a relationship between each pair of data samples by combining the corresponding features in an optimal way [1]. A score is then assigned to each pair to evaluate its relevance forming a global ranking list across all pairs. The success of learning to rank solutions has brought a wide spectrum of applications, including online advertising [2], natural language processing [3] and multimedia retrieval [4]. Learning appropriate data representation and a suitable scoring function are two vital steps in the ranking problem. T raditionally, a feature mapping models the data distribution in a latent space to match the relevance relationship, while the scoring function is used to quantify the relevance measure [1]; however, the ranking problem in the real world emerges from multiple facets and data patterns are mined from diverse domains.

Positive--unlabeled (PU) learning considers two samples, a positive set $P$ with observations from only one class and an unlabeled set $U$ with observations from two classes. The goal is to classify observations in $U$. Class mixture proportion estimation (MPE) in $U$ is a key step in PU learning. In this paper, we show that PU learning is a generalization of local False Discovery Rate estimation. Further we show that PU learning MPE can be reduced to a one--dimensional problem via construction of a classifier trained on the $P$ and $U$ data sets. These observations enable application of methodology from the multiple testing literature to the PU learning problem. In particular we adapt ideas from Storey [2002] and Patra and Sen [2015] to address parameter identifiability and MPE. We prove consistency of two mixture proportion estimators using bounds from empirical process theory, develop tuning parameter free implementations, and demonstrate that they have competitive performance on simulated waveform data and a protein signaling problem.

The Ising model is important in statistical modeling and inference in many applications, however its normalizing constant, mean number of active vertices and mean spin interaction are intractable. We provide accurate approximations that make it possible to calculate these quantities numerically. Simulation studies indicate good performance when compared to Markov Chain Monte Carlo methods and at a tiny fraction of the time. The methodology is also used to perform Bayesian inference in a functional Magnetic Resonance Imaging activation detection experiment.

Deep generative models provide a systematic way to learn nonlinear data distributions through a set of latent variables and a nonlinear "generator" function that maps latent points into the input space. The nonlinearity of the generator implies that the latent space gives a distorted view of the input space. Under mild conditions, we show that this distortion can be characterized by a stochastic Riemannian metric, and we demonstrate that distances and interpolants are significantly improved under this metric. This in turn improves probability distributions, sampling algorithms and clustering in the latent space. Our geometric analysis further reveals that current generators provide poor variance estimates and we propose a new generator architecture with vastly improved variance estimates. Results are demonstrated on convolutional and fully connected variational autoencoders, but the formalism easily generalizes to other deep generative models.

We focus on the problem of estimating the change in the dependency structures of two $p$-dimensional Gaussian Graphical models (GGMs). Previous studies for sparse change estimation in GGMs involve expensive and difficult non-smooth optimization. We propose a novel method, DIFFEE for estimating DIFFerential networks via an Elementary Estimator under a high-dimensional situation. DIFFEE is solved through a faster and closed form solution that enables it to work in large-scale settings. We conduct a rigorous statistical analysis showing that surprisingly DIFFEE achieves the same asymptotic convergence rates as the state-of-the-art estimators that are much more difficult to compute. Our experimental results on multiple synthetic datasets and one real-world data about brain connectivity show strong performance improvements over baselines, as well as significant computational benefits.