Reliable uncertainty estimation for time series prediction is critical in many fields, including physics, biology, and manufacturing. At Uber, probabilistic time series forecasting is used for robust prediction of number of trips during special events, driver incentive allocation, as well as real-time anomaly detection across millions of metrics. Classical time series models are often used in conjunction with a probabilistic formulation for uncertainty estimation. However, such models are hard to tune, scale, and add exogenous variables to. Motivated by the recent resurgence of Long Short Term Memory networks, we propose a novel end-to-end Bayesian deep model that provides time series prediction along with uncertainty estimation. We provide detailed experiments of the proposed solution on completed trips data, and successfully apply it to large-scale time series anomaly detection at Uber.

Let's visualize to improve your prediction... Let us say, you are writing a nice and clean Machine Learning code (e.g. You code is OK, first you divided your dataset into two parts, "Training Set and Testing Set" as usual with the function like train_test_split and with some random factor. Your prediction could be slightly under or overfit, like the figures below. As the name of the suggests, cross-validation is the next fun thing after learning Linear Regression because it helps to improve your prediction using the K-Fold strategy. What is K-Fold you asked?

Summary: Dealing with imbalanced datasets is an everyday problem. SMOTE, Synthetic Minority Oversampling TEchnique and its variants are techniques for solving this problem through oversampling that have recently become a very popular way to improve model performance. There are some problems that never go away. Imbalanced datasets is one in which the majority case greatly outweighs the minority case. Years ago we dealt with this by naïve oversampling or, if we had enough data, even under sampling to get the dataset more in balance.

Jim Moynes, vice president of risk management at Ford Motor Credit in Dearborn, Mich., first became interested in using machine learning to improve car loan underwriting several years ago. "We were watching what others were working on," he said. "We like to be innovative and try to stay up with what's going on." The company recently ran an experiment to see if machine learning could help its underwriters better understand the loan applications it receives. It was a champion vs. challenger test: Moynes' team took several years of loan data, removed all personally identifiable information from it, and gave it to ZestFinance, a provider of machine-learning-based online lending software, and its own modeling team, which creates logistic regression models to predict potential borrowers' creditworthiness. Each team ran the loan application data through its models and predicted the future performance of the loans.

Probabilistic mixture models have been widely used for different machine learning and pattern recognition tasks such as clustering, dimensionality reduction, and classification. In this paper, we focus on trying to solve the most common challenges related to supervised learning algorithms by using mixture probability distribution functions. With this modeling strategy, we identify sub-labels and generate synthetic data in order to reach better classification accuracy. It means we focus on increasing the training data synthetically to increase the classification accuracy.

When applied to training deep neural networks, stochastic gradient descent (SGD) often incurs steady progression phases, interrupted by catastrophic episodes in which loss and gradient norm explode. A possible mitigation of such events is to slow down the learning process. This paper presents a novel approach to control the SGD learning rate, that uses two statistical tests. The first one, aimed at fast learning, compares the momentum of the normalized gradient vectors to that of random unit vectors and accordingly gracefully increases or decreases the learning rate. The second one is a change point detection test, aimed at the detection of catastrophic learning episodes; upon its triggering the learning rate is instantly halved. Both abilities of speeding up and slowing down the learning rate allows the proposed approach, called SALeRA, to learn as fast as possible but not faster. Experiments on standard benchmarks show that SALeRA performs well in practice, and compares favorably to the state of the art.

Similarity-based clustering and semi-supervised learning methods separate the data into clusters or classes according to the pairwise similarity between the data, and the pairwise similarity is crucial for their performance. In this paper, we propose a novel discriminative similarity learning framework which learns discriminative similarity for either data clustering or semi-supervised learning. The proposed framework learns classifier from each hypothetical labeling, and searches for the optimal labeling by minimizing the generalization error of the learned classifiers associated with the hypothetical labeling. Kernel classifier is employed in our framework. By generalization analysis via Rademacher complexity, the generalization error bound for the kernel classifier learned from hypothetical labeling is expressed as the sum of pairwise similarity between the data from different classes, parameterized by the weights of the kernel classifier. Such pairwise similarity serves as the discriminative similarity for the purpose of clustering and semi-supervised learning, and discriminative similarity with similar form can also be induced by the integrated squared error bound for kernel density classification. Based on the discriminative similarity induced by the kernel classifier, we propose new clustering and semi-supervised learning methods. 1 Y. Yang et al.

Given a nonconvex function $f(x)$ that is an average of $n$ smooth functions, we design stochastic first-order methods to find its approximate stationary points. The performance of our new methods depend on the smallest (negative) eigenvalue $-\sigma$ of the Hessian. This parameter $\sigma$ captures how strongly nonconvex $f(x)$ is, and is analogous to the strong convexity parameter for convex optimization. At least in theory, our methods outperform known (offline) methods for a range of parameter $\sigma$, and can also be used to find approximate local minima. Our result implies an interesting dichotomy: there exists a threshold $\sigma_0$ so that the currently fastest methods for $\sigma>\sigma_0$ and for $\sigma<\sigma_0$ have different behaviors: the former scales with $n^{2/3}$ and the latter scales with $n^{3/4}$.

KG: Starting from the beginning, what is statistics and how did it come about? Could you give us a short definition and history of the discipline? In a brief nutshell statistics began as a way to understand the workings of states, productivity, life expectancy, agricultural yields, etc., and to make estimates of things from samples (an statistical example of the latter dates back to the 5th century BCE in Athens). Concerning a definition for statistics, it is a field that is a science unto itself and that benefits all other fields and everyday life. What is unique about statistics is its proven tools for decision making in the face of uncertainty, understanding sources of variation and bias, and most importantly, statistical thinking.

The telecommunications industry is on the verge of a major transformation through the use of advanced analytics and big data technologies like the MapR Converged Data Platform. The MapR Guide to Big Data in Telecommunications is designed to help you understand the trends and technologies behind this data driven telecommunications revolution. In this week's Whiteboard Walkthrough Ted Dunning, Chief Application Architect at MapR, explains in detail how to use streaming IoT sensor data from handsets and devices as well as cell tower data to detect strange anomalies. He takes us from best practices for data architecture, including the advantages of multi-master writes with MapR Streams, through analysis of the telecom data using clustering methods to discover normal and anomalous behaviors. I'd like to talk a little bit about data processing in the context of telecom.