Profiling cellular phenotypes from microscopic imaging can provide meaningful biological information resulting from various factors affecting the cells. One motivating application is drug development: morphological cell features can be captured from images, from which similarities between different drugs applied at different dosages can be quantified. The general approach is to find a function mapping the images to an embedding space of manageable dimensionality whose geometry captures relevant features of the input images. An important known issue for such methods is separating relevant biological signal from nuisance variation. For example, the embedding vectors tend to be more correlated for cells that were cultured and imaged during the same week than for cells from a different week, despite having identical drug compounds applied in both cases. In this case, the particular batch a set of experiments were conducted in constitutes the domain of the data; an ideal set of image embeddings should contain only the relevant biological information (e.g. drug effects). We develop a method for adjusting the image embeddings in order to `forget' domain-specific information while preserving relevant biological information. To do this, we minimize a loss function based on the Wasserstein distance. We find for our transformed embeddings (1) the underlying geometric structure is preserved and (2) less domain-specific information is present.

This paper focuses on the problem of estimating historical traffic volumes between sparselylocated traffic sensors, which transportation agencies need to accurately compute statewide performance measures. To this end, the paper examines applications of vehicle probe data, automatic traffic recorder counts, and neural network models to estimate hourly volumes in the Maryland highway network, and proposes a novel approach that combines neural networks with an existing profiling method. On average, the proposed approach yields 26% more accurate estimates than volume profiles, which are currently used by transportation agencies across the US to compute statewide performance measures. The paper also quantifies the value of using vehicle probe data in estimating hourly traffic volumes, which provides important managerial insights to transportation agencies interested in acquiring this type of data. For example, results show that volumes can be estimated with a mean absolute percent error of about 20% at locations where average number of observed probes is between 30 and 47 vehicles/hr, which provides a useful guideline for assessing the value of probe vehicle data from different vendors. Introduction Hourly traffic volumes and speeds are important inputs needed by transportation agencies for calculating statewide performance measures.

Traditional dictionary learning methods are based on quadratic convex loss function and thus are sensitive to outliers. In this paper, we propose a generic framework for robust dictionary learning based on concave losses. We provide results on composition of concave functions, notably regarding super-gradient computations, that are key for developing generic dictionary learning algorithms applicable to smooth and non-smooth losses. In order to improve identification of outliers, we introduce an initialization heuristic based on undercomplete dictionary learning. Experimental results using synthetic and real data demonstrate that our method is able to better detect outliers, is capable of generating better dictionaries, outperforming state-of-the-art methods such as K-SVD and LC-KSVD.

This paper proposes a method for multi-class classification problems, where the number of classes $K$ is large. The method, referred to as {\em Candidates v.s. Noises Estimation} (CANE), selects a small subset of candidate classes and samples the remaining classes. We show that CANE is always consistent and computationally efficient. Moreover, the resulting estimator has low statistical variance approaching that of the maximum likelihood estimator, when the observed label belongs to the selected candidates with high probability. In practice, we use a tree structure with leaves as classes to promote fast beam search for candidate selection. We also apply the CANE method to estimate word probabilities in neural language models. Experiments show that CANE achieves better prediction accuracy over the Noise-Contrastive Estimation (NCE), its variants and a number of the state-of-the-art tree classifiers, while it gains significant speedup compared to the standard $\mathcal{O}(K)$ methods.

We consider the problem of learning a one-hidden-layer neural network: we assume the input $x\in \mathbb{R}^d$ is from Gaussian distribution and the label $y = a^\top \sigma(Bx) + \xi$, where $a$ is a nonnegative vector in $\mathbb{R}^m$ with $m\le d$, $B\in \mathbb{R}^{m\times d}$ is a full-rank weight matrix, and $\xi$ is a noise vector. We first give an analytic formula for the population risk of the standard squared loss and demonstrate that it implicitly attempts to decompose a sequence of low-rank tensors simultaneously. Inspired by the formula, we design a non-convex objective function $G(\cdot)$ whose landscape is guaranteed to have the following properties: 1. All local minima of $G$ are also global minima. 2. All global minima of $G$ correspond to the ground truth parameters. 3. The value and gradient of $G$ can be estimated using samples. With these properties, stochastic gradient descent on $G$ provably converges to the global minimum and learn the ground-truth parameters. We also prove finite sample complexity result and validate the results by simulations.

Molecular simulations produce very high-dimensional data-sets with millions of data points. As analysis methods are often unable to cope with so many dimensions, it is common to use dimensionality reduction and clustering methods to reach a reduced representation of the data. Yet these methods often fail to capture the most important features necessary for the construction of a Markov model. Here we demonstrate the results of various dimensionality reduction methods on two simulation data-sets, one of protein folding and another of protein-ligand binding. The methods tested include a k-means clustering variant, a non-linear auto encoder, principal component analysis and tICA. The dimension-reduced data is then used to estimate the implied timescales of the slowest process by a Markov state model analysis to assess the quality of the projection. The projected dimensions learned from the data are visualized to demonstrate which conformations the various methods choose to represent the molecular process.

Stochastic gradient descent in continuous time (SGDCT) provides a computationally efficient method for the statistical learning of continuous-time models, which are widely used in science, engineering, and finance. The SGDCT algorithm follows a (noisy) descent direction along a continuous stream of data. The parameter updates occur in continuous time and satisfy a stochastic differential equation. This paper analyzes the asymptotic convergence rate of the SGDCT algorithm by proving a central limit theorem for strongly convex objective functions and, under slightly stronger conditions, for non-convex objective functions as well. An L$^p$ convergence rate is also proven for the algorithm in the strongly convex case.

Hypergraph partitioning is an important problem in machine learning, computer vision and network analytics. A widely used method for hypergraph partitioning relies on minimizing a normalized sum of the costs of partitioning hyperedges across clusters. Algorithmic solutions based on this approach assume that different partitions of a hyperedge incur the same cost. However, this assumption fails to leverage the fact that different subsets of vertices within the same hyperedge may have different structural importance. We hence propose a new hypergraph clustering technique, termed inhomogeneous hypergraph partitioning, which assigns different costs to different hyperedge cuts. We prove that inhomogeneous partitioning produces a quadratic approximation to the optimal solution if the inhomogeneous costs satisfy submodularity constraints. Moreover, we demonstrate that inhomogenous partitioning offers significant performance improvements in applications such as structure learning of rankings, subspace segmentation and motif clustering.

The increasing size and complexity of scientific data could dramatically enhance discovery and prediction for basic scientific applications. Realizing this potential, however, requires novel statistical analysis methods that are both interpretable and predictive. We introduce Union of Intersections (UoI), a flexible, modular, and scalable framework for enhanced model selection and estimation. Methods based on UoI perform model selection and model estimation through intersection and union operations, respectively. We show that UoI-based methods achieve low-variance and nearly unbiased estimation of a small number of interpretable features, while maintaining high-quality prediction accuracy. We perform extensive numerical investigation to evaluate a UoI algorithm ($UoI_{Lasso}$) on synthetic and real data. In doing so, we demonstrate the extraction of interpretable functional networks from human electrophysiology recordings as well as accurate prediction of phenotypes from genotype-phenotype data with reduced features. We also show (with the $UoI_{L1Logistic}$ and $UoI_{CUR}$ variants of the basic framework) improved prediction parsimony for classification and matrix factorization on several benchmark biomedical data sets. These results suggest that methods based on the UoI framework could improve interpretation and prediction in data-driven discovery across scientific fields.

Although a majority of the theoretical literature in high-dimensional statistics has focused on settings which involve fully-observed data, settings with missing values and corruptions are common in practice. We consider the problems of estimation and of constructing component-wise confidence intervals in a sparse high-dimensional linear regression model when some covariates of the design matrix are missing completely at random. We analyze a variant of the Dantzig selector [9] for estimating the regression model and we use a de-biasing argument to construct component-wise confidence intervals. Our first main result is to establish upper bounds on the estimation error as a function of the model parameters (the sparsity level s, the expected fraction of observed covariates $\rho_*$, and a measure of the signal strength $\|\beta^*\|_2$). We find that even in an idealized setting where the covariates are assumed to be missing completely at random, somewhat surprisingly and in contrast to the fully-observed setting, there is a dichotomy in the dependence on model parameters and much faster rates are obtained if the covariance matrix of the random design is known. To study this issue further, our second main contribution is to provide lower bounds on the estimation error showing that this discrepancy in rates is unavoidable in a minimax sense. We then consider the problem of high-dimensional inference in the presence of missing data. We construct and analyze confidence intervals using a de-biased estimator. In the presence of missing data, inference is complicated by the fact that the de-biasing matrix is correlated with the pilot estimator and this necessitates the design of a new estimator and a novel analysis. We also complement our mathematical study with extensive simulations on synthetic and semi-synthetic data that show the accuracy of our asymptotic predictions for finite sample sizes.