We present a framework for accelerating a spectrum of machine learning algorithms that require computation of bilinear inverse forms $u^\top A^{-1}u$, where $A$ is a positive definite matrix and $u$ a given vector. Our framework is built on Gauss-type quadrature and easily scales to large, sparse matrices. Further, it allows retrospective computation of lower and upper bounds on $u^\top A^{-1}u$, which in turn accelerates several algorithms. We prove that these bounds tighten iteratively and converge at a linear (geometric) rate. To our knowledge, ours is the first work to demonstrate these key properties of Gauss-type quadrature, which is a classical and deeply studied topic. We illustrate empirical consequences of our results by using quadrature to accelerate machine learning tasks involving determinantal point processes and submodular optimization, and observe tremendous speedups in several instances.

Given two sets of variables, derived from a common set of samples, sparse Canonical Correlation Analysis (CCA) seeks linear combinations of a small number of variables in each set, such that the induced canonical variables are maximally correlated. Sparse CCA is NP-hard. We propose a novel combinatorial algorithm for sparse diagonal CCA, i.e., sparse CCA under the additional assumption that variables within each set are standardized and uncorrelated. Our algorithm operates on a low rank approximation of the input data and its computational complexity scales linearly with the number of input variables. It is simple to implement, and parallelizable. In contrast to most existing approaches, our algorithm administers precise control on the sparsity of the extracted canonical vectors, and comes with theoretical data-dependent global approximation guarantees, that hinge on the spectrum of the input data. Finally, it can be straightforwardly adapted to other constrained variants of CCA enforcing structure beyond sparsity. We empirically evaluate the proposed scheme and apply it on a real neuroimaging dataset to investigate associations between brain activity and behavior measurements.

Understanding how features interact with each other is of paramount importance in many scientific discoveries and contemporary applications. Yet interaction identification becomes challenging even for a moderate number of covariates. In this paper, we suggest an efficient and flexible procedure, called the interaction pursuit (IP), for interaction identification in ultra-high dimensions. The suggested method first reduces the number of interactions and main effects to a moderate scale by a new feature screening approach, and then selects important interactions and main effects in the reduced feature space using regularization methods. Compared to existing approaches, our method screens interactions separately from main effects and thus can be more effective in interaction screening. Under a fairly general framework, we establish that for both interactions and main effects, the method enjoys the sure screening property in screening and oracle inequalities in selection. Our method and theoretical results are supported by several simulation and real data examples.

State-of-the-art sequence labeling systems traditionally require large amounts of task-specific knowledge in the form of handcrafted features and data pre-processing. In this paper, we introduce a novel neutral network architecture that benefits from both word-and character-level representations automatically, by using combination of bidirectional LSTM, CNN and CRF. Our system is truly end-to-end, requiring no feature engineering or data pre-processing, thus making it applicable to a wide range of sequence labeling tasks. We evaluate our system on two data sets for two sequence labeling tasks -- Penn Treebank WSJ corpus for part-of-speech (POS) tagging and CoNLL 2003 corpus for named entity recognition (NER). We obtain state-of-the-art performance on both datasets -- 97.55% accuracy for POS tagging and 91.21% F1 for NER. 1 Introduction Linguistic sequence labeling, such as part-of- speech (POS) tagging and named entity recognition (NER), is one of the first stages in deep language understanding and its importance has been well recognized in the natural language processing community. Most traditional high performance sequence labeling models are linear statistical models, including Hidden Markov Models (HMM) and Conditional Random Fields (CRF) (Ratinov and Roth, 2009; Passos et al., 2014; Luo et al., 2015), which rely heavily on handcrafted features and task-specific resources. For example, English POS taggers benefit from carefully designed word spelling features; orthographic features and external resources such as gazetteers are widely used in NER. However, such task-specific knowledge is costly to develop (Ma and Xia, 2014), making sequence labeling models difficult to adapt to new tasks or new domains. In the past few years, nonlinear neural networks with as input distributed word representations, also known as word embeddings, have been broadly applied to NLP problems with great success.

Many methods have been proposed for detecting emerging events in text streams using topic modeling. However, these methods have shortcomings that make them unsuitable for rapid detection of locally emerging events on massive text streams. We describe Spatially Compact Semantic Scan (SCSS) that has been developed specifically to overcome the shortcomings of current methods in detecting new spatially compact events in text streams. SCSS employs alternating optimization between using semantic scan (Liu and Neill (2011)) to estimate contrastive foreground topics in documents, and discovering spatial neighborhoods (Shao et al. (2011)) with high occurrence of documents containing the foreground topics. We evaluate our method on Emergency Department chief complaints dataset (ED dataset) to verify the effectiveness of our method in detecting real-world disease outbreaks from free-text ED chief complaint data.

Variational inference (VI) combined with data subsampling enables approximate posterior inference over large data sets, but suffers from poor local optima. We first formulate a deterministic annealing approach for the generic class of conditionally conjugate exponential family models. This approach uses a decreasing temperature parameter which deterministically deforms the objective during the course of the optimization. A well-known drawback to this annealing approach is the choice of the cooling schedule. We therefore introduce variational tempering, a variational algorithm that introduces a temperature latent variable to the model. In contrast to related work in the Markov chain Monte Carlo literature, this algorithm results in adaptive annealing schedules. Lastly, we develop local variational tempering, which assigns a latent temperature to each data point; this allows for dynamic annealing that varies across data. Compared to the traditional VI, all proposed approaches find improved predictive likelihoods on held-out data.

Harlan also noted in the comment below that any truncated kernel density estimator (KDE) from density() in R does not integrate to 1 over its support set. Thanks to Julian Richer Daily for suggesting on AnalyticBridge to scale any truncated kernel density estimator (KDE) from density() by its integral to get a KDE that integrates to 1 over its support set. I have used my own function for trapezoidal integration to do so, and this has been added below. I thank everyone for your patience while I took the time to write a post about numerical integration before posting this correction. I was in the process of moving between jobs and cities when Harlan first brought this issue to my attention, and I had also been planning a major expansion of this blog since then.

"We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances." "When you have two competing theories that make exactly the same predictions, the simpler one is the better." One famous example of Occam's Razor in action is found in conspiracy theories surrounding the NASA moon landings. Many conspiracy theorists believe that the first Moon Landing was staged and filmed in a studio, part of an elaborate hoax. Their justification relies upon many twisted and convoluted theories, whereas the NASA argument is fairly straightforward.

DeepMind, an artificial intelligence company owned by Google, has attempted to justify why it needs access to millions of NHS patient records for a kidney monitoring app, after a new investigation from New Scientist questioned whether an ethical approval process should have been obtained first. The AI research lab, acquired by Google in 2014 for around 400 million, signed a data-sharing agreement with the Royal Free London NHS Foundation Trust on 29 September 2015. The agreement gives Google DeepMind access to the names, addresses, and medical conditions of the 1.6 million patients that are treated at Barnet, Chase Farm, and the Royal Free hospitals each year, as well as data on all patients treated by the Trust in the past five years. This week, New Scientist questioned why Google DeepMind needs access to so much data on so many people, including those who have never experienced kidney problems, for the app, which is called Streams. Streams -- used by Royal Free clinicians in three separate trials since December 2015 -- is designed to detect acute kidney injury (AKI), a condition that kills more than 1,000 people a month.

Ashok Goel wants to expand high-quality education to "millions" more people over the internet. It's the same goal that's pushed universities to make more and more courses and degree programs available over the internet, making it possible for students living on the far sides of the word to get degrees from American universities -- and vice versa. But online education has a problem: Of the hordes of students that sign up for massive open online classes (MOOCs), an average of less than 7% finish. Goel thinks artificial intelligence can change that. "There are many reasons" students don't finish, he told Tech Insider.