We introduce, test and discuss a method for classifying and clustering data modeled as directed graphs. The idea is to start diffusion processes from any subset of a data collection, generating corresponding distributions for reaching points in the network. These distributions take the form of high-dimensional numerical vectors and capture essential topological properties of the original dataset. We show how these diffusion vectors can be successfully applied for getting state-of-the-art accuracies in the problem of extracting pathways from metabolic networks. We also provide a guideline to illustrate how to use our method for classification problems, and discuss important details of its implementation. In particular, we present a simple dimensionality reduction technique that lowers the computational cost of classifying diffusion vectors, while leaving the predictive power of the classification process substantially unaltered. Although the method has very few parameters, the results we obtain show its flexibility and power. This should make it helpful in many other contexts.

Non-linear manifold learning enables high-dimensional data analysis, but requires out-of-sample-extension methods to process new data points. In this paper, we propose a manifold learning algorithm based on deep learning to create an encoder, which maps a high-dimensional dataset and its low-dimensional embedding, and a decoder, which takes the embedded data back to the high-dimensional space. Stacking the encoder and decoder together constructs an autoencoder, which we term a diffusion net, that performs out-of-sample-extension as well as outlier detection. We introduce new neural net constraints for the encoder, which preserves the local geometry of the points, and we prove rates of convergence for the encoder. Also, our approach is efficient in both computational complexity and memory requirements, as opposed to previous methods that require storage of all training points in both the high-dimensional and the low-dimensional spaces to calculate the out-of-sample-extension and the pre-image.

Gene expression levels in a population vary extensively across tissues. Such heterogeneity is caused by genetic variability and environmental factors, and is expected to be linked to disease development. The abundance of experimental data now enables the identification of features of gene expression profiles that are shared across tissues, and those that are tissue-specific. While most current research is concerned with characterising differential expression by comparing mean expression profiles across tissues, it is also believed that a significant difference in a gene expression's variance across tissues may also be associated to molecular mechanisms that are important for tissue development and function. We propose a sparse multi-view matrix factorisation (sMVMF) algorithm to jointly analyse gene expression measurements in multiple tissues, where each tissue provides a different "view" of the underlying organism. The proposed methodology can be interpreted as an extension of principal component analysis in that it provides the means to decompose the total sample variance in each tissue into the sum of two components: one capturing the variance that is shared across tissues, and one isolating the tissue-specific variances. sMVMF has been used to jointly model mRNA expression profiles in three tissues - adipose, skin and LCL - which are available for a large and well-phenotyped twins cohort, TwinsUK. Using sMVMF, we are able to prioritise genes based on whether their variation patterns are specific to each tissue. Furthermore, using DNA methylation profiles available, we provide supporting evidence that adipose-specific gene expression patterns may be driven by epigenetic effects.

We present a novel approach to automatically segment magnetic resonance (MR) images of the human brain into anatomical regions. Our methodology is based on a deep artificial neural network that assigns each voxel in an MR image of the brain to its corresponding anatomical region. The inputs of the network capture information at different scales around the voxel of interest: 3D and orthogonal 2D intensity patches capture the local spatial context while large, compressed 2D orthogonal patches and distances to the regional centroids enforce global spatial consistency. Contrary to commonly used segmentation methods, our technique does not require any non-linear registration of the MR images. To benchmark our model, we used the dataset provided for the MICCAI 2012 challenge on multi-atlas labelling, which consists of 35 manually segmented MR images of the brain. We obtained competitive results (mean dice coefficient 0.725, error rate 0.163) showing the potential of our approach. To our knowledge, our technique is the first to tackle the anatomical segmentation of the whole brain using deep neural networks.

Most real-world networks exhibit community structure, a phenomenon characterized by existence of node clusters whose intra-edge connectivity is stronger than edge connectivities between nodes belonging to different clusters. In addition to facilitating a better understanding of network behavior, community detection finds many practical applications in diverse settings. Communities in online social networks are indicative of shared functional roles, or affiliation to a common socio-economic status, the knowledge of which is vital for targeted advertisement. In buyer-seller networks, community detection facilitates better product recommendations. Unfortunately, reliability of community assignments is hindered by anomalous user behavior often observed as unfair self-promotion, or "fake" highly-connected accounts created to promote fraud. The present paper advocates a novel approach for jointly tracking communities while detecting such anomalous nodes in time-varying networks. By postulating edge creation as the result of mutual community participation by node pairs, a dynamic factor model with anomalous memberships captured through a sparse outlier matrix is put forth. Efficient tracking algorithms suitable for both online and decentralized operation are developed. Experiments conducted on both synthetic and real network time series successfully unveil underlying communities and anomalous nodes.

Spectral clustering is a technique that clusters elements using the top few eigenvectors of their (possibly normalized) similarity matrix. The quality of spectral clustering is closely tied to the convergence properties of these principal eigenvectors. This rate of convergence has been shown to be identical for both the normalized and unnormalized variants in recent random matrix theory literature. However, normalization for spectral clustering is commonly believed to be beneficial [Stat. Comput. 17 (2007) 395-416]. Indeed, our experiments show that normalization improves prediction accuracy. In this paper, for the popular stochastic blockmodel, we theoretically show that normalization shrinks the spread of points in a class by a constant fraction under a broad parameter regime. As a byproduct of our work, we also obtain sharp deviation bounds of empirical principal eigenvalues of graphs generated from a stochastic blockmodel.

Many online companies sell advertisement space in second-price auctions with reserve. In this paper, we develop a probabilistic method to learn a profitable strategy to set the reserve price. We use historical auction data with features to fit a predictor of the best reserve price. This problem is delicate - the structure of the auction is such that a reserve price set too high is much worse than a reserve price set too low. To address this we develop objective variables, a new framework for combining probabilistic modeling with optimal decision-making. Objective variables are "hallucinated observations" that transform the revenue maximization task into a regularized maximum likelihood estimation problem, which we solve with an EM algorithm. This framework enables a variety of prediction mechanisms to set the reserve price. As examples, we study objective variable methods with regression, kernelized regression, and neural networks on simulated and real data. Our methods outperform previous approaches both in terms of scalability and profit.

Microbial identification is a central issue in microbiology, in particular in the fields of infectious diseases diagnosis and industrial quality control. The concept of species is tightly linked to the concept of biological and clinical classification where the proximity between species is generally measured in terms of evolutionary distances and/or clinical phenotypes. Surprisingly, the information provided by this well-known hierarchical structure is rarely used by machine learning-based automatic microbial identification systems. Structured machine learning methods were recently proposed for taking into account the structure embedded in a hierarchy and using it as additional a priori information, and could therefore allow to improve microbial identification systems. We test and compare several state-of-the-art machine learning methods for microbial identification on a new Matrix-Assisted Laser Desorption/Ionization Time-of-Flight mass spectrometry (MALDI-TOF MS) dataset. We include in the benchmark standard and structured methods, that leverage the knowledge of the underlying hierarchical structure in the learning process. Our results show that although some methods perform better than others, structured methods do not consistently perform better than their "flat" counterparts. We postulate that this is partly due to the fact that standard methods already reach a high level of accuracy in this context, and that they mainly confuse species close to each other in the tree, a case where using the known hierarchy is not helpful.

Energy price forecasting is a relevant yet hard task in the field of multi-step time series forecasting. In this paper we compare a well-known and established method, ARMA with exogenous variables with a relatively new technique Gradient Boosting Regression. The method was tested on data from Global Energy Forecasting Competition 2014 with a year long rolling window forecast. The results from the experiment reveal that a multi-model approach is significantly better performing in terms of error metrics. Gradient Boosting can deal with seasonality and auto-correlation out-of-the box and achieve lower rate of normalized mean absolute error on real-world data.

We describe the neural-network training framework used in the Kaldi speech recognition toolkit, which is geared towards training DNNs with large amounts of training data using multiple GPU-equipped or multi-core machines. In order to be as hardware-agnostic as possible, we needed a way to use multiple machines without generating excessive network traffic. Our method is to average the neural network parameters periodically (typically every minute or two), and redistribute the averaged parameters to the machines for further training. Each machine sees different data. By itself, this method does not work very well. However, we have another method, an approximate and efficient implementation of Natural Gradient for Stochastic Gradient Descent (NG-SGD), which seems to allow our periodic-averaging method to work well, as well as substantially improving the convergence of SGD on a single machine.