The group affect or emotion in an image of people can be inferred by extracting features about both the people in the picture and the overall makeup of the scene. The state-of-the-art on this problem investigates a combination of facial features, scene extraction and even audio tonality. This paper combines three additional modalities, namely, human pose, text-based tagging and CNN extracted features / predictions. To the best of our knowledge, this is the first time all of the modalities were extracted using deep neural networks. We evaluate the performance of our approach against baselines and identify insights throughout this paper.

Period estimation is one of the central topics in astronomical time series analysis, where data is often unevenly sampled. Especially challenging are studies of stellar magnetic cycles, as there the periods looked for are of the order of the same length than the datasets themselves. The datasets often contain trends, the origin of which is either a real long-term cycle or an instrumental effect, but these effects cannot be reliably separated, while they can lead to erroneous period determinations if not properly handled. In this study we aim at developing a method that can handle the trends properly, and by performing extensive set of testing, we show that this is the optimal procedure when contrasted with methods that do not include the trend directly to the model. The effect of the form of the noise (whether constant or heteroscedastic) on the results is also investigated. We introduce a Bayesian Generalised Lomb-Scargle Periodogram with Trend (BGLST), which is a probabilistic linear regression model using Gaussian priors for the coefficients and uniform prior for the frequency parameter. We show, using synthetic data, that when there is no prior information on whether and to what extent the true model of the data contains a linear trend, the introduced BGLST method is preferable to the methods which either detrend the data or leave the data untrended before fitting the periodic model. Whether to use noise with different than constant variance in the model depends on the density of the data sampling as well as on the true noise type of the process.

The abundance of high-dimensional data in the modern sciences has generated tremendous interest in penalized estimators such as the lasso, scaled lasso, square-root lasso, elastic net, and many others. In this paper, we establish a general oracle inequality for prediction in high-dimensional linear regression with such methods. Since the proof relies only on convexity and continuity arguments, the result holds irrespective of the design matrix and applies to a wide range of penalized estimators. Overall, the bound demonstrates that generic estimators can provide consistent prediction with any design matrix. From a practical point of view, the bound can help to identify the potential of specific estimators, and they can help to get a sense of the prediction accuracy in a given application.

We develop a multi-kernel based regression method for graph signal processing where the target signal is assumed to be smooth over a graph. In multi-kernel regression, an effective kernel function is expressed as a linear combination of many basis kernel functions. We estimate the linear weights to learn the effective kernel function by appropriate regularization based on graph smoothness. We show that the resulting optimization problem is shown to be convex and pro- pose an accelerated projected gradient descent based solution. Simulation results using real-world graph signals show efficiency of the multi-kernel based approach over a standard kernel based approach.

Penalized regression models such as the lasso have been extensively applied to analyzing high-dimensional data sets. However, due to memory limitations, existing R packages like glmnet and ncvreg are not capable of fitting lasso-type models for ultrahigh-dimensional, multi-gigabyte data sets that are increasingly seen in many areas such as genetics, genomics, biomedical imaging, and high-frequency finance. In this research, we implement an R package called biglasso that tackles this challenge. biglasso utilizes memory-mapped files to store the massive data on the disk, only reading data into memory when necessary during model fitting, and is thus able to handle out-of-core computation seamlessly. Moreover, it's equipped with newly proposed, more efficient feature screening rules, which substantially accelerate the computation. Benchmarking experiments show that our biglasso package, as compared to existing popular ones like glmnet, is much more memory- and computation-efficient. We further analyze a 31 GB real data set on a laptop with only 16 GB RAM to demonstrate the out-of-core computation capability of biglasso in analyzing massive data sets that cannot be accommodated by existing R packages.

The analysis of cancer genomic data has long suffered "the curse of dimensionality". Sample sizes for most cancer genomic studies are a few hundreds at most while there are tens of thousands of genomic features studied. Various methods have been proposed to leverage prior biological knowledge, such as pathways, to more effectively analyze cancer genomic data. Most of the methods focus on testing marginal significance of the associations between pathways and clinical phenotypes. They can identify relevant pathways, but do not involve predictive modeling. In this article, we propose a Pathway-based Kernel Boosting (PKB) method for integrating gene pathway information for sample classification, where we use kernel functions calculated from each pathway as base learners and learn the weights through iterative optimization of the classification loss function. We apply PKB and several competing methods to three cancer studies with pathological and clinical information, including tumor grade, stage, tumor sites, and metastasis status. Our results show that PKB outperforms other methods, and identifies pathways relevant to the outcome variables.

The age of big data has produced data sets that are computationally expensive to analyze and store. Algorithmic leveraging proposes that we sample observations from the original data set to generate a representative data set and then perform analysis on the representative data set. In this paper, we present efficient algorithms for constructing finite sample confidence intervals for each algorithmic leveraging estimated regression coefficient, with asymptotic coverage guarantees. In simulations, we confirm empirically that the confidence intervals have the desired coverage probabilities, while bootstrap confidence intervals may not.

TL;DR I cover how cross-validation is a somewhat tricky problem for matrix factorization models (including PCA & clustering as special cases) and provide some Python code snippets for fitting these models with held out data. Cross-validation is a fundamental paradigm in modern data analysis. However, it is largely applied to supervised settings, such as regression and classification. Here, the procedure is simple: fit your model on, say, 90% of the data (the training set), and evaluate its performance on the remaining 10% (the test set). However, this idea does not easily extend to other unsupervised methods, such as dimensionality reduction methods or clustering.

In this paper, we introduce a new learning strategy based on a seminal idea of Mojirsheibani (1999, 2000, 2002a, 2002b), who proposed a smart method for combining several classifiers, relying on a consensus notion. In many aggregation methods, the prediction for a new observation x is computed by building a linear or convex combination over a collection of basic estimators r1(x),. .. , rm(x) previously calibrated using a training data set. Mojirsheibani proposes to compute the prediction associated to a new observation by combining selected outputs of the training examples. The output of a training example is selected if some kind of consensus is observed: the predictions computed for the training example with the different machines have to be "similar" to the prediction for the new observation. This approach has been recently extended to the context of regression in Biau et al. (2016). In the original scheme, the agreement condition is actually required to hold for all individual estimators, which appears inadequate if there is one bad initial estimator. In practice, a few disagreements are allowed ; for establishing the theoretical results, the proportion of estimators satisfying the condition is required to tend to 1. In this paper, we propose an alternative procedure, mixing the previous consensus ideas on the predictions with the Euclidean distance computed between entries. This may be seen as an alternative approach allowing to reduce the effect of a possibly bad estimator in the initial list, using a constraint on the inputs. We prove the consistency of our strategy in classification and in regression. We also provide some numerical experiments on simulated and real data to illustrate the benefits of this new aggregation method. On the whole, our practical study shows that our method may perform much better than the original combination technique, and, in particular, exhibit far less variance. We also show on simulated examples that this procedure mixing inputs and outputs is still robust to high dimensional inputs.

Aberrations in complex biological systems develop in the background of diverse genetic and environmental factors and are associated with multiple complex molecular events. These include changes in the genome, transcriptome, proteome and metabolome, as well as epigenetic effects. Advances in high-throughput profiling techniques have enabled a systematic and comprehensive exploration of the genetic and epigenetic basis of various diseases, including cancer (Kaushik et al., 2016; Lee et al., 2016), diabetes (Sas et al., 2018; Yuan et al., 2014), chronic kidney disease (Atzler et al., 2014), etc. Further, such multi-Omics collections have become available for patients belonging to different, but related disease subtypes, with The Cancer Genome Atlas (TCGA: Tomczak et al. (2015)) being a prototypical one. Hence, there is an increasing need for models that can integrate such complex data both vertically across multiple modalities and horizontally across different disease subtypes. Figure 1 provides a schematic representation of the horizontal and vertical structure of such heterogeneous multi-modal Omics data as outlined above.