Canonical correlation analysis (CCA) is a classical and important multivariate technique for exploring the relationship between two sets of continuous variables. CCA has applications in many fields, such as genomics and neuroimaging. It can extract meaningful features as well as use these features for subsequent analysis. Although some sparse CCA methods have been developed to deal with high-dimensional problems, they are designed specifically for continuous data and do not consider the integer-valued data from next-generation sequencing platforms that exhibit very low counts for some important features. We propose a model-based probabilistic approach for correlation and canonical correlation estimation for two sparse count data sets (PSCCA). PSCCA demonstrates that correlations and canonical correlations estimated at the natural parameter level are more appropriate than traditional estimation methods applied to the raw data. We demonstrate through simulation studies that PSCCA outperforms other standard correlation approaches and sparse CCA approaches in estimating the true correlations and canonical correlations at the natural parameter level. We further apply the PSCCA method to study the association of miRNA and mRNA expression data sets from a squamous cell lung cancer study, finding that PSCCA can uncover a large number of strongly correlated pairs than standard correlation and other sparse CCA approaches.

Subsampling of received wireless signals is important for relaxing hardware requirements as well as the computational cost of signal processing algorithms that rely on the output samples. We propose a subsampling technique to facilitate the use of deep learning for automatic modulation classification in wireless communication systems. Unlike traditional approaches that rely on pre-designed strategies that are solely based on expert knowledge, the proposed data-driven subsampling strategy employs deep neural network architectures to simulate the effect of removing candidate combinations of samples from each training input vector, in a manner inspired by how wrapper feature selection models work. The subsampled data is then processed by another deep learning classifier that recognizes each of the considered 10 modulation types. We show that the proposed subsampling strategy not only introduces drastic reduction in the classifier training time, but can also improve the classification accuracy to higher levels than those reached before for the considered dataset. An important feature herein is exploiting the transferability property of deep neural networks to avoid retraining the wrapper models and obtain superior performance through an ensemble of wrappers over that possible through solely relying on any of them. Automatic modulation classification plays an important role in modern wireless communications. It finds applications in various commercial and military areas. For example, Software Defined Radios (SDR) use blind recognition of the modulation type to quickly adapt to various communication systems, without requiring control overhead. In military settings, friendly signals should be securely received, while hostile signals need to be efficiently recognized typically without prior information.

Neural networks have seen limited use in prediction for high-dimensional data with small sample sizes, because they tend to overfit and require tuning many more hyperparameters than existing off-the-shelf machine learning methods. With small modifications to the network architecture and training procedure, we show that dense neural networks can be a practical data analysis tool in these settings. The proposed method, Ensemble by Averaging Sparse-Input Hierarchical networks (EASIER-net), appropriately prunes the network structure by tuning only two L1-penalty parameters, one that controls the input sparsity and another that controls the number of hidden layers and nodes. The method selects variables from the true support if the irrelevant covariates are only weakly correlated with the response; otherwise, it exhibits a grouping effect, where strongly correlated covariates are selected at similar rates. On a collection of real-world datasets with different sizes, EASIER-net selected network architectures in a data-adaptive manner and achieved higher prediction accuracy than off-the-shelf methods on average.

Motivation: Real-world data often contain measurements with both continuous and discrete values. Despite the availability of many libraries, data sets with mixed data types require intensive pre-processing steps, and it remains a challenge to describe the relationships between variables. The data understanding phase is an important step in the data mining process, however, without making any assumptions on the data, the search space is super-exponential in the number of variables. Methods: We propose graphical hypergeometric networks (HNet), a method to test associations across variables for significance using statistical inference. The aim is to determine a network using only the significant associations in order to shed light on the complex relationships across variables. HNet processes raw unstructured data sets and outputs a network that consists of (partially) directed or undirected edges between the nodes (i.e., variables). To evaluate the accuracy of HNet, we used well known data sets and in addition generated data sets with known ground truth. The performance of HNet is compared to Bayesian structure learning. Results: We demonstrate that HNet showed high accuracy and performance in the detection of node links. In the case of the Alarm data set we can demonstrate on average an MCC score of 0.33 + 0.0002 (P<1x10-6), whereas Bayesian structure learning resulted in an average MCC score of 0.52 + 0.006 (P<1x10-11), and randomly assigning edges resulted in a MCC score of 0.004 + 0.0003 (P=0.49). Conclusions: HNet can process raw unstructured data sets, allows analysis of mixed data types, it easily scales up in number of variables, and allows detailed examination of the detected associations. Availability: https://erdogant.github.io/hnet/

Transfer learning research attempts to make model induction transferable across different domains. This method assumes that specific information regarding to which domain each instance belongs is known. This paper helps to extend the capability of transfer learning for linear regression problems to situations where the domain information is uncertain or unknown; in fact, the framework can be extended to classification problems. For normal datasets, we assume that some latent domain information is available for transfer learning. The instances in each domain can be inferred by different parameters. We obtain this domain information from the distribution of the regression coefficients corresponding to the explanatory variable $x$ as well as the response variable $y$ based on a Dirichlet process, which is more reasonable. As a result, we transfer not only variable $x$ as usual but also variable $y$, which is challenging since the testing data have no response value. Previous work mainly overcomes the problem via pseudo-labelling based on transductive learning, which introduces serious bias. We provide a novel framework for analysing the problem and considering this general situation: the joint distribution of variable $x$ and variable $y$. Furthermore, our method controls the bias well compared with previous work. We perform linear regression on the new feature space that consists of different latent domains and the target domain, which is from the testing data. The experimental results show that the proposed model performs well on real datasets.

Recent advances in biological research have seen the emergence of high-throughput technologies with numerous applications that allow the study of biological mechanisms at an unprecedented depth and scale. A large amount of genomic data is now distributed through consortia like The Cancer Genome Atlas (TCGA), where specific types of biological information on specific type of tissue or cell are available. In cancer research, the challenge is now to perform integrative analyses of high-dimensional multi-omic data with the goal to better understand genomic processes that correlate with cancer outcomes, e.g. elucidate gene networks that discriminate a specific cancer subgroups (cancer sub-typing) or discovering gene networks that overlap across different cancer types (pan-cancer studies). In this paper, we propose a novel mixed graphical model approach to analyze multi-omic data of different types (continuous, discrete and count) and perform model selection by extending the Birth-Death MCMC (BDMCMC) algorithm initially proposed by \citet{stephens2000bayesian} and later developed by \cite{mohammadi2015bayesian}. We compare the performance of our method to the LASSO method and the standard BDMCMC method using simulations and find that our method is superior in terms of both computational efficiency and the accuracy of the model selection results. Finally, an application to the TCGA breast cancer data shows that integrating genomic information at different levels (mutation and expression data) leads to better subtyping of breast cancers.

Large-sample data became prevalent as data acquisition became cheaper and easier. While a large sample size has theoretical advantages for many statistical methods, it presents computational challenges. Sketching, or compression, is a well-studied approach to address these issues in regression settings, but considerably less is known about its performance in classification settings. Here we consider the computational issues due to large sample size within the discriminant analysis framework. We propose a new compression approach for reducing the number of training samples for linear and quadratic discriminant analysis, in contrast to existing compression methods which focus on reducing the number of features. We support our approach with a theoretical bound on the misclassification error rate compared to the Bayes classifier. Empirical studies confirm the significant computational gains of the proposed method and its superior predictive ability compared to random sub-sampling.

Bayesian method is capable of capturing real world uncertainties/incompleteness and properly addressing the over-fitting issue faced by deep neural networks. In recent years, Bayesian Neural Networks (BNNs) have drawn tremendous attentions of AI researchers and proved to be successful in many applications. However, the required high computation complexity makes BNNs difficult to be deployed in computing systems with limited power budget. In this paper, an efficient BNN inference flow is proposed to reduce the computation cost then is evaluated by means of both software and hardware implementations. A feature decomposition and memorization (\texttt{DM}) strategy is utilized to reform the BNN inference flow in a reduced manner. About half of the computations could be eliminated compared to the traditional approach that has been proved by theoretical analysis and software validations. Subsequently, in order to resolve the hardware resource limitations, a memory-friendly computing framework is further deployed to reduce the memory overhead introduced by \texttt{DM} strategy. Finally, we implement our approach in Verilog and synthesise it with 45 $nm$ FreePDK technology. Hardware simulation results on multi-layer BNNs demonstrate that, when compared with the traditional BNN inference method, it provides an energy consumption reduction of 73\% and a 4$\times$ speedup at the expense of 14\% area overhead.

In this paper we propose Policy Synthesis under probabilistic Constraints (PSyCo), a systematic engineering method for synthesizing safe policies under probabilistic constraints with reinforcement learning and Bayesian model checking. As an implementation of PSyCo we introduce Safe Neural Evolutionary Strategies (SNES). SNES leverages Bayesian model checking while learning to adjust the Lagrangian of a constrained optimization problem derived from a PSyCo specification. We empirically evaluate SNES' ability to synthesize feasible policies in settings with formal safety requirements.

Inferring models, predicting the future, and estimating the entropy rate of discrete-time, discrete-event processes is well-worn ground. However, a much broader class of discrete-event processes operates in continuous-time. Here, we provide new methods for inferring, predicting, and estimating them. The methods rely on an extension of Bayesian structural inference that takes advantage of neural network's universal approximation power. Based on experiments with complex synthetic data, the methods are competitive with the state-of-the-art for prediction and entropy-rate estimation.