Time series are widely used as signals in many classification/regression tasks. It is ubiquitous that time series contains many missing values. Given multiple correlated time series data, how to fill in missing values and to predict their class labels? Existing imputation methods often impose strong assumptions of the underlying data generating process, such as linear dynamics in the state space. In this paper, we propose BRITS, a novel method based on recurrent neural networks for missing value imputation in time series data. Our proposed method directly learns the missing values in a bidirectional recurrent dynamical system, without any specific assumption. The imputed values are treated as variables of RNN graph and can be effectively updated during the backpropagation.BRITS has three advantages: (a) it can handle multiple correlated missing values in time series; (b) it generalizes to time series with nonlinear dynamics underlying; (c) it provides a data-driven imputation procedure and applies to general settings with missing data.We evaluate our model on three real-world datasets, including an air quality dataset, a health-care data, and a localization data for human activity. Experiments show that our model outperforms the state-of-the-art methods in both imputation and classification/regression accuracies.

Distributed stochastic gradient descent is an important subroutine in distributed learning. A setting of particular interest is when the clients are mobile devices, where two important concerns are communication efficiency and the privacy of the clients. Several recent works have focused on reducing the communication cost or introducing privacy guarantees, but none of the proposed communication efficient methods are known to be privacy preserving and none of the known privacy mechanisms are known to be communication efficient. To this end, we study algorithms that achieve both communication efficiency and differential privacy. For $d$ variables and $n \approx d$ clients, the proposed method uses $O(\log \log(nd))$ bits of communication per client per coordinate and ensures constant privacy. We also extend and improve previous analysis of the \emph{Binomial mechanism} showing that it achieves nearly the same utility as the Gaussian mechanism, while requiring fewer representation bits, which can be of independent interest.

A hyperbolic space has been shown to be more capable of modeling complex networks than a Euclidean space. This paper proposes an explicit update rule along geodesics in a hyperbolic space. The convergence of our algorithm is theoretically guaranteed, and the convergence rate is better than the conventional Euclidean gradient descent algorithm. Moreover, our algorithm avoids the "bias" problem of existing methods using the Riemannian gradient. Experimental results demonstrate the good performance of our algorithm in the \Poincare embeddings of knowledge base data.

The goal of a recommendation system is to predict the interest of a user in a given item by exploiting the existing set of ratings as well as certain user/item features. A standard approach to modeling this problem is Inductive Matrix Completion where the predicted rating is modeled as an inner product of the user and the item features projected onto a latent space. In order to learn the parameters effectively from a small number of observed ratings, the latent space is constrained to be low-dimensional which implies that the parameter matrix is constrained to be low-rank. However, such bilinear modeling of the ratings can be limiting in practice and non-linear prediction functions can lead to significant improvements. A natural approach to introducing non-linearity in the prediction function is to apply a non-linear activation function on top of the projected user/item features. Imposition of non-linearities further complicates an already challenging problem that has two sources of non-convexity: a) low-rank structure of the parameter matrix, and b) non-linear activation function. We show that one can still solve the non-linear Inductive Matrix Completion problem using gradient descent type methods as long as the solution is initialized well. That is, close to the optima, the optimization function is strongly convex and hence admits standard optimization techniques, at least for certain activation functions, such as Sigmoid and tanh. We also highlight the importance of the activation function and show how ReLU can behave significantly differently than say a sigmoid function. Finally, we apply our proposed technique to recommendation systems and semi-supervised clustering, and show that our method can lead to much better performance than standard linear Inductive Matrix Completion methods.

Embedding complex objects as vectors in low dimensional spaces is a longstanding problem in machine learning. We propose in this work an extension of that approach, which consists in embedding objects as elliptical probability distributions, namely distributions whose densities have elliptical level sets. We endow these measures with the 2-Wasserstein metric, with two important benefits: (i) For such measures, the squared 2-Wasserstein metric has a closed form, equal to the sum of the squared Euclidean distance between means and the squared Bures metric between covariance matrices. The latter is a Riemannian metric between positive semi-definite matrices, which turns out to be Euclidean on a suitable factor representation of such matrices, which is valid on the entire geodesic between these matrices. (ii) The 2-Wasserstein distance boils down to the usual Euclidean metric when comparing Diracs, and therefore provides the natural framework to extend point embeddings. We show that for these reasons Wasserstein elliptical embeddings are more intuitive and yield tools that are better behaved numerically than the alternative choice of Gaussian embeddings with the Kullback-Leibler divergence. In particular, and unlike previous work based on the KL geometry, we learn elliptical distributions that are not necessarily diagonal. We demonstrate the interest of elliptical embeddings by using them for visualization, to compute embeddings of words, and to reflect entanglement or hypernymy.

When techniques like linear regression or time series were aimed at modelling the general trend exhibited by a set or series of data points, data scientists faced another question - though these models can capture the overall trend but how can one model the volatility in the data? In real life, the initial stages in a business or a new market are always volatile and changing with a high velocity until things calm down and become saturated. It is then one can apply the statistical techniques such as time series analysis or regression as the case may be. To go into the turbulent seas of volatile data and analyze it in a time changing setting, ARCH models were developed. As I already mentioned, ARCH is a statistical model for time series data.

Recently, during my coursework, I have been left in awe of the advancements in the field of science in general. In just about a decade, we have completely revolutionized the way we look at the capabilities of machines, the way we build software and much more. Tasks that seemed impossible just a decade ago have become accessible and effortless. Long story short, we have made the machines think!! Sounds cool, isn't it? Artificial Intelligence has truly entered the mainstream consciousness.

Linear models, as their name implies, relates an outcome to a set of predictors of interest using linear assumptions. Regression models, a subset of linear models, are the most important statistical analysis tool in a data scientist's toolkit. This course covers regression analysis, least squares and inference using regression models. Special cases of the regression model, ANOVA and ANCOVA will be covered as well. Analysis of residuals and variability will be investigated.

Prerequisites: No prerequisites, knowledge of some undergraduate level mathematics would help but is not mandatory. Working knowledge of Python would be helpful if you want to run the source code that is provided. Taught by a Stanford-educated, ex-Googler and an IIT, IIM - educated ex-Flipkart lead analyst. This team has decades of practical experience in quant trading, analytics and e-commerce. The course is shy but confident: It is authoritative, drawn from decades of practical experience -but shies away from needlessly complicating stuff.

During my first project in McKinsey in 2011, I served the CEO of a bank regarding his small business strategy. I wanted to run a linear regression on the bank's data but my boss told me: "Don't do it. Artificial Intelligence is the most general-purpose technology of our time. New products and processes are being developed thanks to better vision systems, speech recognition technologies or recommendation engines based on Machine Learning. In fact, most recent advances in Artificial Intelligence have been achieved in the area of Machine Learning. Long before McKinsey, in 2004, I started my career as a mobile software developer. At that time I had to write precise instructions for every step of my code. Developing the voice recognition system of today's phones would have been tedious and error-prone back then. It would have required literally hundreds of thousands of detailed instructions to codify every single step, including identifying phonemes from sound waves, grouping them into ...