In this paper we study the problem of learning Rectified Linear Units (ReLUs) which are functions of the form $max(0,)$ with $w$ denoting the weight vector. We study this problem in the high-dimensional regime where the number of observations are fewer than the dimension of the weight vector. We assume that the weight vector belongs to some closed set (convex or nonconvex) which captures known side-information about its structure. We focus on the realizable model where the inputs are chosen i.i.d.~from a Gaussian distribution and the labels are generated according to a planted weight vector. We show that projected gradient descent, when initialization at 0, converges at a linear rate to the planted model with a number of samples that is optimal up to numerical constants. Our results on the dynamics of convergence of these very shallow neural nets may provide some insights towards understanding the dynamics of deeper architectures.

We provide a comprehensive study of the convergence of forward-backward algorithm under suitable geometric conditions leading to fast rates. We present several new results and collect in a unified view a variety of results scattered in the literature, often providing simplified proofs. Novel contributions include the analysis of infinite dimensional convex minimization problems, allowing the case where minimizers might not exist. Further, we analyze the relation between different geometric conditions, and discuss novel connections with a priori conditions in linear inverse problems, including source conditions, restricted isometry properties and partial smoothness.

We study the problem of learning to choose from m discrete treatment options (e.g., news item or medical drug) the one with best causal effect for a particular instance (e.g., user or patient) where the training data consists of passive observations of covariates, treatment, and the outcome of the treatment. The standard approach to this problem is regress and compare: split the training data by treatment, fit a regression model in each split, and, for a new instance, predict all m outcomes and pick the best. By reformulating the problem as a single learning task rather than m separate ones, we propose a new approach based on recursively partitioning the data into regimes where different treatments are optimal. We extend this approach to an optimal partitioning approach that finds a globally optimal partition, achieving a compact, interpretable, and impactful personalization model. We develop new tools for validating and evaluating personalization models on observational data and use these to demonstrate the power of our novel approaches in a personalized medicine and a job training application.

We propose a generic Markov Chain Monte Carlo (MCMC) algorithm to speed up computations for datasets with many observations. A key feature of our approach is the use of the highly efficient difference estimator from the survey sampling literature to estimate the log-likelihood accurately using only a small fraction of the data. Our algorithm improves on the $O(n)$ complexity of regular MCMC by operating over local data clusters instead of the full sample when computing the likelihood. The likelihood estimate is used in a Pseudo-marginal framework to sample from a perturbed posterior which is within $O(m^{-1/2})$ of the true posterior, where $m$ is the subsample size. The method is applied to a logistic regression model to predict firm bankruptcy for a large data set. We document a significant speed up in comparison to the standard MCMC on the full dataset.

We introduce the task of Visual Dialog, which requires an AI agent to hold a meaningful dialog with humans in natural, conversational language about visual content. Specifically, given an image, a dialog history, and a question about the image, the agent has to ground the question in image, infer context from history, and answer the question accurately. Visual Dialog is disentangled enough from a specific downstream task so as to serve as a general test of machine intelligence, while being grounded in vision enough to allow objective evaluation of individual responses and benchmark progress. We develop a novel two-person chat data-collection protocol to curate a large-scale Visual Dialog dataset (VisDial). VisDial v0.9 has been released and contains 1 dialog with 10 question-answer pairs on ~120k images from COCO, with a total of ~1.2M dialog question-answer pairs. We introduce a family of neural encoder-decoder models for Visual Dialog with 3 encoders -- Late Fusion, Hierarchical Recurrent Encoder and Memory Network -- and 2 decoders (generative and discriminative), which outperform a number of sophisticated baselines. We propose a retrieval-based evaluation protocol for Visual Dialog where the AI agent is asked to sort a set of candidate answers and evaluated on metrics such as mean-reciprocal-rank of human response. We quantify gap between machine and human performance on the Visual Dialog task via human studies. Putting it all together, we demonstrate the first 'visual chatbot'! Our dataset, code, trained models and visual chatbot are available on https://visualdialog.org

Machine learning is a technology that has grown to prominence over the past ten years (as at this time of writing) and is fast paving the way for the "Age of Automation". This post provides a holistic view of the vital constituents that characterizes machine learning. At the end of this piece, the reader can be able to grasp the major landmarks and foundation stones of the field. Also, this overview provides a structured framework to wade deeper into murkier waters without getting overly overwhelmed. Machine learning is a set of computational tools and mathematical techniques for predicting the future state or classifying the outcomes of a particular variable (or unit of measurement) based on its interactions with other variables in a data set.

Welcome to a new section in our Machine Learning Tutorial series: Deep Learning with Neural Networks and TensorFlow. The artificial neural network is a biologically-inspired methodology to conduct machine learning, intended to mimic your brain (a biological neural network). The Artificial Neural Network, which I will now just refer to as a neural network, is not a new concept. The idea has been around since the 1940's, and has had a few ups and downs, most notably when compared against the Support Vector Machine (SVM). For example, the Neural Network was popularized up until the mid 90s when it was shown that the SVM, using a new-to-the-public (the technique itself was thought up long before it was actually put to use) technique, the "Kernel Trick," was capable of working with non-linearly separable datasets.

If your event rate is around 17% and you say that at 50% cutoff you're getting a very good classification, there's something fishy! How can a logistic model trained to fit only 17% be better than what information the dataset has? Unless, you're measure of accuracy of fit is different from misclassification! Remember, the model usually fits the remaining 83% well, so the misclassification there would be low as compared to the 17%. But I'm unsure how you're getting a 50% cutoff more accurate in terms of misclassification - since, a decrease here, is going to increase it there. The best way to find out the cutoff is by plotting for different values as already suggested, but it's usually got to be around the event rate!

Other major examples include Google's DeepMind Health, which last year announced multiple UK-based partnerships, including with Moorfields Eye Hospital in London, in which they're developing technology to address macular degeneration in aging eyes. Image credit: Google DeepMind Health – An OCT scan of one of the DeepMind Health team's eyes In the area of brain-based diseases like depression, Oxford's P1vital Predicting Response to Depression Treatment (PReDicT) project is using predictive analytics to help diagnose and provide treatment, with the overall goal of producing a commercially-available emotional test battery for use in clinical settings. Key players in this domain include the MIT Clinical Machine Learning Group, whose precision medicine research is focused on the development of algorithms to better understand disease processes and design for effective treatment of diseases like Type 2 diabetes. Until that day comes, Google's DeepMind Health is working with University College London Hospital (UCLH) to develop machine learning algorithms capable of detecting differences in healthy and cancerous tissues to help improve radiation treatments.

The other day I was reading an article on how AI has progressed so far and where it is going. I was awestruck and had a hard time digesting the picture the author drew on possibilities in the future. Here is how I reacted. "A surgeon could control a machine scalpel with her motor cortex instead of holding one in her hand, and she could receive sensory input from that scalpel so that it would feel like an 11th finger to her. So it would be as if one of her fingers was a scalpel and she could do the surgery without holding any tools, giving her much finer control over her incisions. An inexperienced surgeon performing a tough operation could bring a couple of her mentors into the scene as she operates to watch her work through her eyes and think instructions or advice to her. And if something goes really wrong, one of them could "take the wheel" and connect their motor cortex to her outputs to take control of her hands."