Modern recommendation systems can be broadly divided into two key stages: the ranking stage, where the system predicts various user engagements (e.g., click-through rate, like rate, follow rate, watch time), and the value model stage, which aggregates these predictive scores through a function (e.g., a linear combination defined by a weight vector) to measure the value of each content by a single numerical score. Both stages play roughly equally important roles in real industrial systems; however, how to optimize the model weights for the second stage still lacks systematic study. This paper focuses on optimizing the second stage through auto-tuning technology. Although general auto-tuning systems and solutions - both from established production practices and open-source solutions - can address this problem, they typically require weeks or even months to identify a feasible solution. Such prolonged tuning processes are unacceptable in production environments for recommendation systems, as suboptimal value models can severely degrade user experience. An effective auto-tuning solution is required to identify a viable model within 2-3 days, rather than the extended timelines typically associated with existing approaches. In this paper, we introduce a practical auto-tuning system named HyperZero that addresses these time constraints while effectively solving the unique challenges inherent in modern recommendation systems. Moreover, this framework has the potential to be expanded to broader tuning tasks within recommendation systems.

Recent years have witnessed an exponential growth of model scale in deep learning-based recommender systems---from Google's 2016 model with 1 billion parameters to the latest Facebook's model with 12 trillion parameters. Significant quality boost has come with each jump of the model capacity, which makes us believe the era of 100 trillion parameters is around the corner. However, the training of such models is challenging even within industrial scale data centers. We resolve this challenge by careful co-design of both optimization algorithm and distributed system architecture. Specifically, to ensure both the training efficiency and the training accuracy, we design a novel hybrid training algorithm, where the embedding layer and the dense neural network are handled by different synchronization mechanisms; then we build a system called Persia (short for parallel recommendation training system with hybrid acceleration) to support this hybrid training algorithm. Both theoretical demonstrations and empirical studies with up to 100 trillion parameters have been conducted to justify the system design and implementation of Persia. We make Persia publicly available (at github.com/PersiaML/Persia) so that anyone can easily train a recommender model at the scale of 100 trillion parameters.

MOTIVATION: Drosophila melanogaster is a major model organism for investigating the function and interconnection of animal genes in the earliest stages of embryogenesis. Today, images capturing Drosophila gene expression patterns are being produced at a higher throughput than ever before. The analysis of spatial patterns of gene expression is most biologically meaningful when images from a similar time point during development are compared. Thus, the critical first step is to determine the developmental stage of an embryo. This information is also needed to observe and analyze expression changes over developmental time. Currently, developmental stages (time) of embryos in images capturing spatial expression pattern are annotated manually, which is time- and labor-intensive. Embryos are often designated into stage ranges, making the information on developmental time course. This makes downstream analyses inefficient and biological interpretations of similarities and differences in spatial expression patterns challenging, particularly when using automated tools for analyzing expression patterns of large number of images. RESULTS: Here, we present a new computational approach to annotate developmental stage for Drosophila embryos in the gene expression images. In an analysis of 3724 images, the new approach shows high accuracy in predicting the developmental stage correctly (79%). In addition, it provides a stage score that enables one to more finely annotate each embryo so that they are divided into early and late periods of development within standard stage demarcations. Stage scores for all images containing expression patterns of the same gene enable a direct way to view expression changes over developmental time for any gene. We show that the genomewide-expression-maps generated using images from embryos in refined stages illuminate global gene activities and changes much better, and more refined stage annotations improve our ability to better interpret results when expression pattern matches are discovered between genes. AVAILABILITY AND IMPLEMENTATION: The software package is availablefor download at: http://www.public.asu.edu/*jye02/Software/Fly-Project/.

We consider the following signal recovery problem: given a measurement matrix Φ∈\mathbbR^n\times p and a noisy observation vector c∈\mathbbR^n constructed from c = Φθ^* + εwhere ε∈\mathbbR^n is the noise vector whose entries follow i.i.d. centered sub-Gaussian distribution, how to recover the signal θ^* if Dθ^* is sparse \rca under a linear transformation D∈\mathbbR^m\times p? One natural method using convex optimization is to solve the following problem: $\min_θ 1\over 2\|Φθ- c\|^2 + λ\|Dθ\|_1. This paper provides an upper bound of the estimate error and shows the consistency property of this method by assuming that the design matrix Φis a Gaussian random matrix. Specifically, we show 1) in the noiseless case, if the condition number of D is bounded and the measurement number n≥Ω(s\log(p)) where s is the sparsity number, then the true solution can be recovered with high probability; and 2) in the noisy case, if the condition number of D is bounded and the measurement increases faster than s\log(p), that is, s\log(p)=o(n), the estimate error converges to zero with probability 1 when p and s go to infinity. Our results are consistent with those for the special case D=\boldI_p\times p (equivalently LASSO) and improve the existing analysis. The condition number of D plays a critical role in our analysis. We consider the condition numbers in two cases including the fused LASSO and the random graph: the condition number in the fused LASSO case is bounded by a constant, while the condition number in the random graph case is bounded with high probability if m\over p (i.e., #\textedge\over #\textvertex$) is larger than a certain constant. Numerical simulations are consistent with our theoretical results.

With the advances and increasing sophistication in data collection techniques, we are facing with large amounts of data collected from multiple heterogeneous sources in many applications. For example, in the study of Alzheimer's Disease (AD), different types of measurements such as neuroimages, gene/protein expression data, genetic data etc. are often collected and analyzed together for improved predictive power. It is believed that a joint learning of multiple data sources is beneficial as different data sources may contain complementary information, and feature-pruning and data source selection are critical for learning interpretable models from high-dimensional data. Very often the collected data comes with block-wise missing entries; for example, a patient without the MRI scan will have no information in the MRI data block, making his/her overall record incomplete. There has been a growing interest in the data mining community on expanding traditional techniques for single-source complete data analysis to the study of multi-source incomplete data. The key challenge is how to effectively integrate information from multiple heterogeneous sources in the presence of block-wise missing data. In this paper we first investigate the situation of complete data and present a unified ``bi-level" learning model for multi-source data. Then we give a natural extension of this model to the more challenging case with incomplete data. Our major contributions are threefold: (1) the proposed models handle both feature-level and source-level analysis in a unified formulation and include several existing feature learning approaches as special cases; (2) the model for incomplete data avoids direct imputation of the missing elements and thus provides superior performances. Moreover, it can be easily generalized to other applications with block-wise missing data sources; (3) efficient optimization algorithms are presented for both the complete and incomplete models. We have performed comprehensive evaluations of the proposed models on the application of AD diagnosis. Our proposed models compare favorably against existing approaches.

Traditionally, feature construction and feature selection are two important but separate processes in data mining. However, many real world applications require an integrated approach for creating, refining and selecting features. To address this problem, we propose FeaFiner (short for Feature Refiner), an efficient formulation that simultaneously generalizes low-level features into higher level concepts and then selects relevant concepts based on the target variable. Specifically, we formulate a double sparsity optimization problem that identifies groups in the low-level features, generalizes higher level features using the groups and performs feature selection. Since in many clinical researches non- overlapping groups are preferred for better interpretability, we further improve the formulation to generalize features using mutually exclusive feature groups. The proposed formulation is challenging to solve due to the orthogonality constraints, non-convexity objective and non-smoothness penal- ties. We apply a recently developed augmented Lagrangian method to solve this formulation in which each subproblem is solved by a non-monotone spectral projected gradient method. Our numerical experiments show that this approach is computationally efficient and also capable of producing solutions of high quality. We also present a generalization bound showing the consistency and the asymptotic behavior of the learning process of our proposed formulation.

BACKGROUND: Drosophila melanogaster has been established as a model organism for investigating the developmental gene interactions. The spatio-temporal gene expression patterns of Drosophila melanogaster can be visualized by in situ hybridization and documented as digital images. Automated and efficient tools for analyzing these expression images will provide biological insights into the gene functions, interactions, and networks. To facilitate pattern recognition and comparison, many web-based resources have been created to conduct comparative analysis based on the body part keywords and the associated images. With the fast accumulation of images from high-throughput techniques, manual inspection of images will impose a serious impediment on the pace of biological discovery. It is thus imperative to design an automated system for efficient image annotation and comparison. RESULTS: We present a computational framework to perform anatomical keywords annotation for Drosophila gene expression images. The spatial sparse coding approach is used to represent local patches of images in comparison with the well-known bag-of-words (BoW) method. Three pooling functions including max pooling, average pooling and Sqrt (square root of mean squared statistics) pooling are employed to transform the sparse codes to image features. Based on the constructed features, we develop both an image-level scheme and a group-level scheme to tackle the key challenges in annotating Drosophila gene expression pattern images automatically. To deal with the imbalanced data distribution inherent in image annotation tasks, the undersampling method is applied together with majority vote. Results on Drosophila embryonic expression pattern images verify the efficacy of our approach. CONCLUSION: In our experiment, the three pooling functions perform comparably well in feature dimension reduction. The undersampling with majority vote is shown to be effective in tackling the problem of imbalanced data. Moreover, combining sparse coding and image-level scheme leads to consistent performance improvement in keywords annotation.

The group Lasso is an extension of the Lasso for feature selection on (predefined) nonoverlapping groups of features. The nonoverlapping group structure limits its applicability in practice. There have been several recent attempts to study a more general formulation where groups of features are given, potentially with overlaps between the groups. The resulting optimization is, however, much more challenging to solve due to the group overlaps. In this paper, we consider the efficient optimization of the overlapping group Lasso penalized problem. We reveal several key properties of the proximal operator associated with the overlapping group Lasso, and compute the proximal operator by solving the smooth and convex dual problem, which allows the use of the gradient descent type of algorithms for the optimization. Our methods and theoretical results are then generalized to tackle the general overlapping group Lasso formulation based on the l(q) norm. We further extend our algorithm to solve a nonconvex overlapping group Lasso formulation based on the capped norm regularization, which reduces the estimation bias introduced by the convex penalty. We have performed empirical evaluations using both a synthetic and the breast cancer gene expression dataset, which consists of 8,141 genes organized into (overlapping) gene sets. Experimental results show that the proposed algorithm is more efficient than existing state-of-the-art algorithms. Results also demonstrate the effectiveness of the nonconvex formulation for overlapping group Lasso.

High-dimensional regression/classification continues to be an important and challenging problem, especially when features are highly correlated. Feature selection, combined with additional structure information on the features has been considered to be promising in promoting regression/classification performance. Graph-guided fused lasso (GFlasso) has recently been proposed to facilitate feature selection and graph structure exploitation, when features exhibit certain graph structures. However, the formulation in GFlasso relies on pairwise sample correlations to perform feature grouping, which could introduce additional estimation bias. In this paper, we propose three new feature grouping and selection methods to resolve this issue. The first method employs a convex function to penalize the pairwise l∞ norm of connected regression/classification coefficients, achieving simultaneous feature grouping and selection. The second method improves the first one by utilizing a non-convex function to reduce the estimation bias. The third one is the extension of the second method using a truncated l1 regularization to further reduce the estimation bias. The proposed methods combine feature grouping and feature selection to enhance estimation accuracy. We employ the alternating direction method of multipliers (ADMM) and difference of convex functions (DC) programming to solve the proposed formulations. Our experimental results on synthetic data and two real datasets demonstrate the effectiveness of the proposed methods.

Incomplete data present serious problems when integrating largescale brain imaging data sets from different imaging modalities. In the Alzheimer's Disease Neuroimaging Initiative (ADNI), for example, over half of the subjects lack cerebrospinal fluid (CSF) measurements; an independent half of the subjects do not have fluorodeoxyglucose positron emission tomography (FDG-PET) scans; many lack proteomics measurements. Traditionally, subjects with missing measures are discarded, resulting in a severe loss of available information. We address this problem by proposing two novel learning methods where all the samples (with at least one available data source) can be used. In the first method, we divide our samples according to the availability of data sources, and we learn shared sets of features with state-of-the-art sparse learning methods. Our second method learns a base classifier for each data source independently, based on which we represent each source using a single column of prediction scores; we then estimate the missing prediction scores, which, combined with the existing prediction scores, are used to build a multi-source fusion model. To illustrate the proposed approaches, we classify patients from the ADNI study into groups with Alzheimer's disease (AD), mild cognitive impairment (MCI) and normal controls, based on the multi-modality data. At baseline, ADNI's 780 participants (172 AD, 397 MCI, 211 Normal), have at least one of four data types: magnetic resonance imaging (MRI), FDG-PET, CSF and proteomics. These data are used to test our algorithms. Comprehensive experiments show that our proposed methods yield stable and promising results.

BACKGROUND: Fruit fly embryogenesis is one of the best understood animal development systems, and the spatiotemporal gene expression dynamics in this process are captured by digital images. Analysis of these high-throughput images will provide novel insights into the functions, interactions, and networks of animal genes governing development. To facilitate comparative analysis, web-based interfaces have been developed to conduct image retrieval based on body part keywords and images. Currently, the keyword annotation of spatiotemporal gene expression patterns is conducted manually. However, this manual practice does not scale with the continuously expanding collection of images. In addition, existing image retrieval systems based on the expression patterns may be made more accurate using keywords. RESULTS: In this article, we adapt advanced data mining and computer vision techniques to address the key challenges in annotating and retrieving fruit fly gene expression pattern images. To boost the performance of image annotation and retrieval, we propose representations integrating spatial information and sparse features, overcoming the limitations of prior schemes. CONCLUSIONS: We perform systematic experimental studies to evaluate the proposed schemes in comparison with current methods. Experimental results indicate that the integration of spatial information and sparse features lead to consistent performance improvement in image annotation, while for the task of retrieval, sparse features alone yields better results.

Alzheimer's Disease (AD), the most common type of dementia, is a severe neurodegenerative disorder. Identifying markers that can track the progress of the disease has recently received increasing attentions in AD research. A definitive diagnosis of AD requires autopsy confirmation, thus many clinical/cognitive measures including Mini Mental State Examination (MMSE) and Alzheimer's Disease Assessment Scale cognitive subscale (ADAS-Cog) have been designed to evaluate the cognitive status of the patients and used as important criteria for clinical diagnosis of probable AD. In this paper, we propose a multi-task learning formulation for predicting the disease progression measured by the cognitive scores and selecting markers predictive of the progression. Specifically, we formulate the prediction problem as a multi-task regression problem by considering the prediction at each time point as a task. We capture the intrinsic relatedness among different tasks by a temporal group Lasso regularizer. The regularizer consists of two components including an L2,1-norm penalty on the regression weight vectors, which ensures that a small subset of features will be selected for the regression models at all time points, and a temporal smoothness term which ensures a small deviation between two regression models at successive time points. We have performed extensive evaluations using various types of data at the baseline from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database for predicting the future MMSE and ADAS-Cog scores. Our experimental studies demonstrate the effectiveness of the proposed algorithm for capturing the progression trend and the cross-sectional group differences of AD severity. Results also show that most markers selected by the proposed algorithm are consistent with findings from existing cross-sectional studies.

The group Lasso is an extension of the Lasso for feature selection on (predefined) non-overlapping groups of features. The non-overlapping group structure limits its applicability in practice. There have been several recent attempts to study a more general formulation, where groups of features are given, potentially with overlaps between the groups. The resulting optimization is, however, much more challenging to solve due to the group overlaps. In this paper, we consider the efficient optimization of the overlapping group Lasso penalized problem. We reveal several key properties of the proximal operator associated with the overlapping group Lasso, and compute the proximal operator by solving the smooth and convex dual problem, which allows the use of the gradient descent type of algorithms for the optimization. We have performed empirical evaluations using both synthetic and the breast cancer gene expression data set, which consists of 8,141 genes organized into (overlapping) gene sets. Experimental results show that the proposed algorithm is more efficient than existing state-of-the-art algorithms.

The fused Lasso penalty enforces sparsity in both the coefficients and their successive differences, which is desirable for applications with features ordered in some meaningful way. The resulting problem is, however, challenging to solve, as the fused Lasso penalty is both non-smooth and non-separable. Existing algorithms have high computational complexity and do not scale to large-size problems. In this paper, we propose an Efficient Fused Lasso Algorithm (EFLA) for optimizing this class of problems. One key building block in the proposed EFLA is the Fused Lasso Signal Approximator (FLSA). To efficiently solve FLSA, we propose to reformulate it as the problem of finding an "appropriate" subgradient of the fused penalty at the minimizer, and develop a Subgradient Finding Algorithm (SFA). We further design a restart technique to accelerate the convergence of SFA, by exploiting the special "structures" of both the original and the reformulated FLSA problems. Our empirical evaluations show that, both SFA and EFLA significantly outperform existing solvers. We also demonstrate several applications of the fused Lasso.

The Drosophila gene expression pattern images document the spatial and temporal dynamics of gene expression and they are valuable tools for explicating the gene functions, interaction, and networks during Drosophila embryogenesis. To provide text-based pattern searching, the images in the Berkeley Drosophila Genome Project (BDGP) study are annotated with ontology terms manually by human curators. We present a systematic approach for automating this task, because the number of images needing text descriptions is now rapidly increasing. We consider both improved feature representation and novel learning formulation to boost the annotation performance. For feature representation, we adapt the bag-of-words scheme commonly used in visual recognition problems so that the image group information in the BDGP study is retained. Moreover, images from multiple views can be integrated naturally in this representation. To reduce the quantization error caused by the bag-of-words representation, we propose an improved feature representation scheme based on the sparse learning technique. In the design of learning formulation, we propose a local regularization framework that can incorporate the correlations among terms explicitly. We further show that the resulting optimization problem admits an analytical solution. Experimental results show that the representation based on sparse learning outperforms the bag-of-words representation significantly. Results also show that incorporation of the term-term correlations improves the annotation performance consistently.