We develop a general framework for distribution-free predictive inference in regression, using conformal inference. The proposed methodology allows for the construction of a prediction band for the response variable using any estimator of the regression function. The resulting prediction band preserves the consistency properties of the original estimator under standard assumptions, while guaranteeing finite-sample marginal coverage even when these assumptions do not hold. We analyze and compare, both empirically and theoretically, the two major variants of our conformal framework: full conformal inference and split conformal inference, along with a related jackknife method. These methods offer different tradeoffs between statistical accuracy (length of resulting prediction intervals) and computational efficiency. As extensions, we develop a method for constructing valid in-sample prediction intervals called {\it rank-one-out} conformal inference, which has essentially the same computational efficiency as split conformal inference. We also describe an extension of our procedures for producing prediction bands with locally varying length, in order to adapt to heteroskedascity in the data. Finally, we propose a model-free notion of variable importance, called {\it leave-one-covariate-out} or LOCO inference. Accompanying this paper is an R package {\tt conformalInference} that implements all of the proposals we have introduced. In the spirit of reproducibility, all of our empirical results can also be easily (re)generated using this package.

The goal of unsupervised representation learning is to extract a new representation of data, such that solving many different tasks becomes easier. Existing methods typically focus on vectorized data and offer little support for relational data, which additionally describe relationships among instances. In this work we introduce an approach for relational unsupervised representation learning. Viewing a relational dataset as a hypergraph, new features are obtained by clustering vertices and hyperedges. To find a representation suited for many relational learning tasks, a wide range of similarities between relational objects is considered, e.g. feature and structural similarities. We experimentally evaluate the proposed approach and show that models learned on such latent representations perform better, have lower complexity, and outperform the existing approaches on classification tasks.

At Flickr, we understand that the value in our image corpus is only unlocked when our members can find photos and photographers that inspire them, so we strive to enable the discovery and appreciation of new photos. To further that effort, today we are introducing similarity search on Flickr. If you hover over a photo on a search result page, you will reveal a "…" button that exposes a menu that gives you the option to search for photos similar to the photo you are currently viewing. In many ways, photo search is very different from traditional web or text search. First, the goal of web search is usually to satisfy a particular information need, while with photo search the goal is often one of discovery; as such, it should be delightful as well as functional.

We consider support recovery in the quadratic logistic regression setting - where the target depends on both p linear terms $x_i$ and up to $p^2$ quadratic terms $x_i x_j$. Quadratic terms enable prediction/modeling of higher-order effects between features and the target, but when incorporated naively may involve solving a very large regression problem. We consider the sparse case, where at most $s$ terms (linear or quadratic) are non-zero, and provide a new faster algorithm. It involves (a) identifying the weak support (i.e. all relevant variables) and (b) standard logistic regression optimization only on these chosen variables. The first step relies on a novel insight about correlation tests in the presence of non-linearity, and takes $O(pn)$ time for $n$ samples - giving potentially huge computational gains over the naive approach. Motivated by insights from the boolean case, we propose a non-linear correlation test for non-binary finite support case that involves hashing a variable and then correlating with the output variable. We also provide experimental results to demonstrate the effectiveness of our methods.

This paper presents a novel method for structural data recognition using a large number of graph models. In general, prevalent methods for structural data recognition have two shortcomings: 1) Only a single model is used to capture structural variation. 2) Naive recognition methods are used, such as the nearest neighbor method. In this paper, we propose strengthening the recognition performance of these models as well as their ability to capture structural variation. The proposed method constructs a large number of graph models and trains decision trees using the models. This paper makes two main contributions. The first is a novel graph model that can quickly perform calculations, which allows us to construct several models in a feasible amount of time. The second contribution is a novel approach to structural data recognition: graph model boosting. Comprehensive structural variations can be captured with a large number of graph models constructed in a boosting framework, and a sophisticated classifier can be formed by aggregating the decision trees. Consequently, we can carry out structural data recognition with powerful recognition capability in the face of comprehensive structural variation. The experiments shows that the proposed method achieves impressive results and outperforms existing methods on datasets of IAM graph database repository.

It is usual to consider data protection and learnability as conflicting objectives. This is not always the case: we show how to jointly control inference --- seen as the attack --- and learnability by a noise-free process that mixes training examples, the Crossover Process (cp). One key point is that the cp~is typically able to alter joint distributions without touching on marginals, nor altering the sufficient statistic for the class. In other words, it saves (and sometimes improves) generalization for supervised learning, but can alter the relationship between covariates --- and therefore fool measures of nonlinear independence and causal inference into misleading ad-hoc conclusions. For example, a cp~can increase / decrease odds ratios, bring fairness or break fairness, tamper with disparate impact, strengthen, weaken or reverse causal directions, change observed statistical measures of dependence. For each of these, we quantify changes brought by a cp, as well as its statistical impact on generalization abilities via a new complexity measure that we call the Rademacher cp~complexity. Experiments on a dozen readily available domains validate the theory.

We propose a novel coding theoretic framework for mitigating stragglers in distributed learning. We show how carefully replicating data blocks and coding across gradients can provide tolerance to failures and stragglers for Synchronous Gradient Descent. We implement our schemes in python (using MPI) to run on Amazon EC2, and show how we compare against baseline approaches in running time and generalization error.

Very often features come with their own vectorial descriptions which provide detailed information about their properties. We refer to these vectorial descriptions as feature side-information. In the standard learning scenario, input is represented as a vector of features and the feature side-information is most often ignored or used only for feature selection prior to model fitting. We believe that feature side-information which carries information about features intrinsic property will help improve model prediction if used in a proper way during learning process. In this paper, we propose a framework that allows for the incorporation of the feature side-information during the learning of very general model families to improve the prediction performance. We control the structures of the learned models so that they reflect features similarities as these are defined on the basis of the side-information. We perform experiments on a number of benchmark datasets which show significant predictive performance gains, over a number of baselines, as a result of the exploitation of the side-information.

We propose Edward, a Turing-complete probabilistic programming language. Edward defines two compositional representations---random variables and inference. By treating inference as a first class citizen, on a par with modeling, we show that probabilistic programming can be as flexible and computationally efficient as traditional deep learning. For flexibility, Edward makes it easy to fit the same model using a variety of composable inference methods, ranging from point estimation to variational inference to MCMC. In addition, Edward can reuse the modeling representation as part of inference, facilitating the design of rich variational models and generative adversarial networks. For efficiency, Edward is integrated into TensorFlow, providing significant speedups over existing probabilistic systems. For example, we show on a benchmark logistic regression task that Edward is at least 35x faster than Stan and 6x faster than PyMC3. Further, Edward incurs no runtime overhead: it is as fast as handwritten TensorFlow.

Many objects in the real world are difficult to describe by a single numerical vector of a fixed length, whereas describing them by a set of vectors is more natural. Therefore, Multiple instance learning (MIL) techniques have been constantly gaining on importance throughout last years. MIL formalism represents each object (sample) by a set (bag) of feature vectors (instances) of fixed length where knowledge about objects (e.g., class label) is available on bag level but not necessarily on instance level. Many standard tools including supervised classifiers have been already adapted to MIL setting since the problem got formalized in late nineties. In this work we propose a neural network (NN) based formalism that intuitively bridges the gap between MIL problem definition and the vast existing knowledge-base of standard models and classifiers. We show that the proposed NN formalism is effectively optimizable by a modified back-propagation algorithm and can reveal unknown patterns inside bags. Comparison to eight types of classifiers from the prior art on a set of 14 publicly available benchmark datasets confirms the advantages and accuracy of the proposed solution.