There is a stark disparity between the step size schedules used in practical large scale machine learning and those that are considered optimal by the theory of stochastic approximation. In theory, most results utilize polynomially decaying learning rate schedules, while, in practice, the "Step Decay" schedule is among the most popular schedules, where the learning rate is cut every constant number of epochs (i.e. this is a geometrically decaying schedule). This work examines the step-decay schedule for the stochastic optimization problem of streaming least squares regression (both in the non-strongly convex and strongly convex case), where we show that a sharp theoretical characterization of an optimal learning rate schedule is far more nuanced than suggested by previous work. We focus specifically on the rate that is achievable when using the final iterate of stochastic gradient descent, as is commonly done in practice. Our main result provably shows that a properly tuned geometrically decaying learning rate schedule provides an exponential improvement (in terms of the condition number) over any polynomially decaying learning rate schedule. We also provide experimental support for wider applicability of these results, including for training modern deep neural networks.

Email has remained a principal form of communication among people, both in enterprise and social settings. With a deluge of emails crowding our mailboxes daily, there is a dire need of smart email systems that can recover important emails and make personalized recommendations. In this work, we study the problem of predicting user triage actions to incoming emails where we take the reply prediction as a working example. Different from existing methods, we formulate the triage action prediction as a recommendation problem and focus on the content-based approach, where the users are represented using the content of current and past emails. We also introduce additional similarity features to further explore the affinities between users and emails. Experiments on the publicly available Avocado email collection demonstrate the advantages of our proposed recommendation framework and our method is able to achieve better performance compared to the state-of-the-art deep recommendation methods. More importantly, we provide valuable insight into the effectiveness of different textual and user representations and show that traditional bag-of-words approaches, with the help from the similarity features, compete favorably with the more advanced neural embedding methods.

Band selection, by choosing a set of representative bands in hyperspectral image (HSI), is an effective method to reduce the redundant information without compromising the original contents. Recently, various unsupervised band selection methods have been proposed, but most of them are based on approximation algorithms which can only obtain suboptimal solutions toward a specific objective function. This paper focuses on clustering-based band selection, and proposes a new framework to solve the above dilemma, claiming the following contributions: 1) An optimal clustering framework (OCF), which can obtain the optimal clustering result for a particular form of objective function under a reasonable constraint. 2) A rank on clusters strategy (RCS), which provides an effective criterion to select bands on existing clustering structure. 3) An automatic method to determine the number of the required bands, which can better evaluate the distinctive information produced by certain number of bands. In experiments, the proposed algorithm is compared to some state-of-the-art competitors. According to the experimental results, the proposed algorithm is robust and significantly outperform the other methods on various data sets.

Stochastic gradient Langevin dynamics (SGLD) is a fundamental algorithm in stochastic optimization. Recent work by Zhang et al. [2017] presents an analysis for the hitting time of SGLD for the first and second order stationary points. The proof in Zhang et al. [2017] is a two-stage procedure through bounding the Cheeger's constant, which is rather complicated and leads to loose bounds. In this paper, using intuitions from stochastic differential equations, we provide a direct analysis for the hitting times of SGLD to the first and second order stationary points. Our analysis is straightforward. It only relies on basic linear algebra and probability theory tools. Our direct analysis also leads to tighter bounds comparing to Zhang et al. [2017] and shows the explicit dependence of the hitting time on different factors, including dimensionality, smoothness, noise strength, and step size effects. Under suitable conditions, we show that the hitting time of SGLD to first-order stationary points can be dimension-independent. Moreover, we apply our analysis to study several important online estimation problems in machine learning, including linear regression, matrix factorization, and online PCA.

Applied Data Scientists throughout various industries are commonly faced with the challenging task of encoding high-cardinality categorical features into digestible inputs for machine learning algorithms. This paper describes a Bayesian encoding technique developed for WeWork's lead scoring engine which outputs the probability of a person touring one of our office spaces based on interaction, enrichment, and geospatial data. We present a paradigm for ensemble modeling which mitigates the need to build complicated preprocessing and encoding schemes for categorical variables. In particular, domain-specific conjugate Bayesian models are employed as base learners for features in a stacked ensemble model. For each column of a categorical feature matrix we fit a problem-specific prior distribution, for example, the Beta distribution for a binary classification problem. In order to analytically derive the moments of the posterior distribution, we update the prior with the conjugate likelihood of the corresponding target variable for each unique value of the given categorical feature. This function of column and value encodes the categorical feature matrix so that the final learner in the ensemble model ingests low-dimensional numerical input. Experimental results on both curated and real world datasets demonstrate impressive accuracy and computational efficiency on a variety of problem archetypes. Particularly, for the lead scoring engine at WeWork -- where some categorical features have as many as 300,000 levels -- we have seen an AUC improvement from 0.87 to 0.97 through implementing conjugate Bayesian model encoding.

The recent adoption of Electronic Health Records (EHRs) by health care providers has introduced an important source of data that provides detailed and highly specific insights into patient phenotypes over large cohorts. These datasets, in combination with machine learning and statistical approaches, generate new opportunities for research and clinical care. However, many methods require the patient representations to be in structured formats, while the information in the EHR is often locked in unstructured texts designed for human readability. In this work, we develop the methodology to automatically extract clinical features from clinical narratives from large EHR corpora without the need for prior knowledge. We consider medical terms and sentences appearing in clinical narratives as atomic information units. We propose an efficient clustering strategy suitable for the analysis of large text corpora and to utilize the clusters to represent information about the patient compactly. To demonstrate the utility of our approach, we perform an association study of clinical features with somatic mutation profiles from 4,007 cancer patients and their tumors. We apply the proposed algorithm to a dataset consisting of about 65 thousand documents with a total of about 3.2 million sentences. We identify 341 significant statistical associations between the presence of somatic mutations and clinical features. We annotated these associations according to their novelty, and report several known associations. We also propose 32 testable hypotheses where the underlying biological mechanism does not appear to be known but plausible. These results illustrate that the automated discovery of clinical features is possible and the joint analysis of clinical and genetic datasets can generate appealing new hypotheses.

As an efficient and scalable graph neural network, GraphSAGE has enabled an inductive capability for inferring unseen nodes or graphs by aggregating subsampled local neighborhoods and by learning in a mini-batch gradient descent fashion. The neighborhood sampling used in GraphSAGE is effective in order to improve computing and memory efficiency when inferring a batch of target nodes with diverse degrees in parallel. Despite this advantage, the default uniform sampling suffers from high variance in training and inference, leading to sub-optimum accuracy. We propose a new data-driven sampling approach to reason about the real-valued importance of a neighborhood by a non-linear regressor, and to use the value as a criterion for subsampling neighborhoods. The regressor is learned using a value-based reinforcement learning. The implied importance for each combination of vertex and neighborhood is inductively extracted from the negative classification loss output of GraphSAGE. As a result, in an inductive node classification benchmark using three datasets, our method enhanced the baseline using the uniform sampling, outperforming recent variants of a graph neural network in accuracy.

Feature crossing captures interactions among categorical features and is useful to enhance learning from tabular data in real-world businesses. In this paper, we present AutoCross, an automatic feature crossing tool provided by 4Paradigm to its customers, ranging from banks, hospitals, to Internet corporations. By performing beam search in a tree-structured space, AutoCross enables efficient generation of high-order cross features, which is not yet visited by existing works. Additionally, we propose successive mini-batch gradient descent and multi-granularity discretization to further improve efficiency and effectiveness, while ensuring simplicity so that no machine learning expertise or tedious hyper-parameter tuning is required. Furthermore, the algorithms are designed to reduce the computational, transmitting, and storage costs involved in distributed computing. Experimental results on both benchmark and real-world business datasets demonstrate the effectiveness and efficiency of AutoCross. It is shown that AutoCross can significantly enhance the performance of both linear and deep models.

Edit distance, also known as Levenshtein distance, is an essential way to compare two strings that proved to be particularly useful in the analysis of genetic sequences and natural language processing. However, edit distance is a discrete function that is known to be hard to optimize. This fact hampers the use of this metric in Machine Learning. Even as simple algorithm as K-means fails to cluster a set of sequences using edit distance if they are of variable length and abundance. In this paper we propose a novel metric - soft edit distance (SED), which is a smooth approximation of edit distance. It is differentiable and therefore it is possible to optimize it with gradient methods. Similar to original edit distance, SED as well as its derivatives can be calculated with recurrent formulas at polynomial time. We prove usefulness of the proposed metric on synthetic datasets and clustering of biological sequences.

Relational learning is concerned with methods that cannot only leverage the attributes of data points but also their relationships. Diagnosing a patient, for example, not only depends on the patient's vitals and demographic information but also on the same information about their relatives, the information about the hospitals they have visited, and so on. Relational learning, therefore, does not make the assumption of independence between data points but models their dependency explicitly. Graphs are a natural way to represent relational information and there is a large number of machine learning algorithms leveraging graph structure. Graph neural networks (GNNs) (Scarselli et al., 2009) are one such class of algorithms that are able to incorporate sparse and discrete dependency structures between data points. While a graph structure is available in some domains, in others it has to be inferred or constructed. A possible approach is to first create a k-nearest neighbor (kNN) graph based on some measure of similarity between data points. This is a common strategy used by several learning methods such as LLE (Roweis & Saul, 2000) and Isomap (Tenenbaum et al., 2000).