We consider forecasting a single time series using high-dimensional predictors in the presence of a possible nonlinear forecast function. The sufficient forecasting (Fan et al., 2016) used sliced inverse regression to estimate lower-dimensional sufficient indices for nonparametric forecasting using factor models. However, Fan et al. (2016) is fundamentally limited to the inverse first-moment method, by assuming the restricted fixed number of factors, linearity condition for factors, and monotone effect of factors on the response. In this work, we study the inverse second-moment method using directional regression and the inverse third-moment method to extend the methodology and applicability of the sufficient forecasting. As the number of factors diverges with the dimension of predictors, the proposed method relaxes the distributional assumption of the predictor and enhances the capability of capturing the non-monotone effect of factors on the response. We not only provide a high-dimensional analysis of inverse moment methods such as exhaustiveness and rate of convergence, but also prove their model selection consistency. The power of our proposed methods is demonstrated in both simulation studies and an empirical study of forecasting monthly macroeconomic data from Q1 1959 to Q1 2016. During our theoretical development, we prove an invariance result for inverse moment methods, which make a separate contribution to the sufficient dimension reduction.

The ubiquitous presence of sequence data across fields such as the web, healthcare, bioinformatics, and text mining has made sequence mining a vital research area. However, sequence mining is particularly challenging because of difficulty in finding (dis)similarity/distance between sequences. This is because a distance measure between sequences is not obvious due to their unstructuredness---arbitrary strings of arbitrary length. Feature representations, such as n-grams, are often used but they either compromise on extracting both short- and long-term sequence patterns or have a high computation. We propose a new function, Sequence Graph Transform (SGT), that extracts the short- and long-term sequence features and embeds them in a finite-dimensional feature space. Importantly, SGT has low computation and can extract any amount of short- to long-term patterns without any increase in the computation, also proved theoretically in this paper. Due to this, SGT yields superior result with significantly higher accuracy and lower computation compared to the existing methods. We show it via several experimentation and SGT's real world application for clustering, classification, search and visualization as examples.

Nutrient-based meal recommendations have the potential to help individuals prevent or manage conditions such as diabetes and obesity. However, learning people's food preferences and making recommendations that simultaneously appeal to their palate and satisfy nutritional expectations are challenging. Existing approaches either only learn high-level preferences or require a prolonged learning period. We propose Yum-me, a personalized nutrient-based meal recommender system designed to meet individuals' nutritional expectations, dietary restrictions, and fine-grained food preferences. Yum-me enables a simple and accurate food preference profiling procedure via a visual quiz-based user interface, and projects the learned profile into the domain of nutritionally appropriate food options to find ones that will appeal to the user. We present the design and implementation of Yum-me, and further describe and evaluate two innovative contributions. The first contriution is an open source state-of-the-art food image analysis model, named FoodDist. We demonstrate FoodDist's superior performance through careful benchmarking and discuss its applicability across a wide array of dietary applications. The second contribution is a novel online learning framework that learns food preference from item-wise and pairwise image comparisons. We evaluate the framework in a field study of 227 anonymous users and demonstrate that it outperforms other baselines by a significant margin. We further conducted an end-to-end validation of the feasibility and effectiveness of Yum-me through a 60-person user study, in which Yum-me improves the recommendation acceptance rate by 42.63%.

Whenever you spot a trend plotted against time, you would be looking at a time series. The de facto choice for studying financial market performance and weather forecasts, time series are one of the most pervasive analysis techniques because of its inextricable relation to time--we are always interested to foretell the future. One intuitive way to make forecasts would be to refer to recent time points. Today's stock prices would likely be more similar to yesterday's prices than those from five years ago. Hence, we would give more weight to recent than to older prices in predicting today's price. These correlations between past and present values demonstrate temporal dependence, which forms the basis of a popular time series analysis technique called ARIMA (Autoregressive Integrated Moving Average).

K-Means procedure - which is a vector quantization method often used as a clustering method - does not explicitly use pairwise distances b/w data points at all (in contrast to hierarchical and some other clusterings which allow for arbitrary proximity measure). It amounts to repeatedly assigning points to the closest centroid thereby using Euclidean distance from data points to a centroid. However, K-Means is implicitly based on pairwise Euclidean distances b/w data points, because the sum of squared deviations from centroid is equal to the sum of pairwise squared Euclidean distances divided by the number of points. The term "centroid" is itself from Euclidean geometry. It is multivariate mean in euclidean space. Euclidean space is about euclidean distances.

In this paper we study the setting where features are added or change interpretation over time, which has applications in multiple domains such as retail, manufacturing, finance. In particular, we propose an approach to provably determine the time instant from which the new/changed features start becoming relevant with respect to an output variable in an agnostic (supervised) learning setting. We also suggest an efficient version of our approach which has the same asymptotic performance. Moreover, our theory also applies when we have more than one such change point. Independent post analysis of a change point identified by our method for a large retailer revealed that it corresponded in time with certain unflattering news stories about a brand that resulted in the change in customer behavior. We also applied our method to data from an advanced manufacturing plant identifying the time instant from which downstream features became relevant. To the best of our knowledge this is the first work that formally studies change point detection in a distribution independent agnostic setting, where the change point is based on the changing relationship between input and output.

Out of nearly 70,000 bills introduced in the U.S. Congress from 2001 to 2015, only 2,513 were enacted. We developed a machine learning approach to forecasting the probability that any bill will become law. Starting in 2001 with the 107th Congress, we trained models on data from previous Congresses, predicted all bills in the current Congress, and repeated until the 113th Congress served as the test. For prediction we scored each sentence of a bill with a language model that embeds legislative vocabulary into a high-dimensional, semantic-laden vector space. This language representation enables our investigation into which words increase the probability of enactment for any topic. To test the relative importance of text and context, we compared the text model to a context-only model that uses variables such as whether the bill's sponsor is in the majority party. To test the effect of changes to bills after their introduction on our ability to predict their final outcome, we compared using the bill text and meta-data available at the time of introduction with using the most recent data. At the time of introduction context-only predictions outperform text-only, and with the newest data text-only outperforms context-only. Combining text and context always performs best. We conducted a global sensitivity analysis on the combined model to determine important variables predicting enactment.

The recent explosion of data set size, in number of records and attributes, has triggered the development of a number of big data platforms as well as parallel data analytics algorithms. At the same time though, it has pushed for usage of data dimensionality reduction procedures. Indeed, more is not always better. Large amounts of data might sometimes produce worse performances in data analytics applications. One of my most recent projects happened to be about churn prediction and to use the 2009 KDD Challenge large data set.

The idea behind hierarchical cluster analysis is to show which of a (potentially large) set of samples are most similar to one another, and to group these similar samples in the same limb of a tree. Each of the samples can be thought of a sitting in an m-dimensional space, defined by the m variables (columns) in the dataframe. We define similarity on the basis of the distance between two samples in this m-dimensional space. Several different distance measures could be used, but the default is Euclidean distance and this is used to work out the distance from every sample to every other sample. This quantitative dissimilarity structure of the data is stored in a matrix produced by the "dist function".

We present a conditional generative model to learn variation in cell and nuclear morphology and the location of subcellular structures from microscopy images. Our model generalizes to a wide range of subcellular localization and allows for a probabilistic interpretation of cell and nuclear morphology and structure localization from fluorescence images. We demonstrate the effectiveness of our approach by producing photo-realistic cell images using our generative model. The conditional nature of the model provides the ability to predict the localization of unobserved structures given cell and nuclear morphology.