This paper studies ordered weighted L1 (OWL) norm regularization for sparse estimation problems with strongly correlated variables. We prove sufficient conditions for clustering based on the correlation/colinearity of variables using the OWL norm, of which the so-called OSCAR is a particular case. Our results extend previous ones for OSCAR in several ways: for the squared error loss, our conditions hold for the more general OWL norm and under weaker assumptions; we also establish clustering conditions for the absolute error loss, which is, as far as we know, a novel result. Furthermore, we characterize the statistical performance of OWL norm regularization for generative models in which certain clusters of regression variables are strongly (even perfectly) correlated, but variables in different clusters are uncorrelated. We show that if the true p-dimensional signal generating the data involves only s of the clusters, then O(s log p) samples suffice to accurately estimate the signal, regardless of the number of coefficients within the clusters. The estimation of s-sparse signals with completely independent variables requires just as many measurements. In other words, using the OWL we pay no price (in terms of the number of measurements) for the presence of strongly correlated variables.

There is a broad range of BioNLP tasks for which active learning (AL) can significantly reduce annotation costs and a specific AL algorithm we have developed is particularly effective in reducing annotation costs for these tasks. We have previously developed an AL algorithm called ClosestInitPA that works best with tasks that have the following characteristics: redundancy in training material, burdensome annotation costs, Support Vector Machines (SVMs) work well for the task, and imbalanced datasets (i.e. when set up as a binary classification problem, one class is substantially rarer than the other). Many BioNLP tasks have these characteristics and thus our AL algorithm is a natural approach to apply to BioNLP tasks.

Sparse high dimensional graphical model selection is a popular topic in contemporary machine learning. To this end, various useful approaches have been proposed in the context of $\ell_1$-penalized estimation in the Gaussian framework. Though many of these inverse covariance estimation approaches are demonstrably scalable and have leveraged recent advances in convex optimization, they still depend on the Gaussian functional form. To address this gap, a convex pseudo-likelihood based partial correlation graph estimation method (CONCORD) has been recently proposed. This method uses coordinate-wise minimization of a regression based pseudo-likelihood, and has been shown to have robust model selection properties in comparison with the Gaussian approach. In direct contrast to the parallel work in the Gaussian setting however, this new convex pseudo-likelihood framework has not leveraged the extensive array of methods that have been proposed in the machine learning literature for convex optimization. In this paper, we address this crucial gap by proposing two proximal gradient methods (CONCORD-ISTA and CONCORD-FISTA) for performing $\ell_1$-regularized inverse covariance matrix estimation in the pseudo-likelihood framework. We present timing comparisons with coordinate-wise minimization and demonstrate that our approach yields tremendous payoffs for $\ell_1$-penalized partial correlation graph estimation outside the Gaussian setting, thus yielding the fastest and most scalable approach for such problems. We undertake a theoretical analysis of our approach and rigorously demonstrate convergence, and also derive rates thereof.

We propose a parsimonious topic model for text corpora. In related models such as Latent Dirichlet Allocation (LDA), all words are modeled topic-specifically, even though many words occur with similar frequencies across different topics. Our modeling determines salient words for each topic, which have topic-specific probabilities, with the rest explained by a universal shared model. Further, in LDA all topics are in principle present in every document. By contrast our model gives sparse topic representation, determining the (small) subset of relevant topics for each document. We derive a Bayesian Information Criterion (BIC), balancing model complexity and goodness of fit. Here, interestingly, we identify an effective sample size and corresponding penalty specific to each parameter type in our model. We minimize BIC to jointly determine our entire model -- the topic-specific words, document-specific topics, all model parameter values, {\it and} the total number of topics -- in a wholly unsupervised fashion. Results on three text corpora and an image dataset show that our model achieves higher test set likelihood and better agreement with ground-truth class labels, compared to LDA and to a model designed to incorporate sparsity.

We consider a problem of grouping multiple graphs into several clusters using singular value thesholding and non-negative factorization. We derive a model selection information criterion to estimate the number of clusters. We demonstrate our approach using "Swimmer data set" as well as simulated data set, and compare its performance with two standard clustering algorithms.

Log-linear models are the popular workhorses of analyzing contingency tables. A log-linear parameterization of an interaction model can be more expressive than a direct parameterization based on probabilities, leading to a powerful way of defining restrictions derived from marginal, conditional and context-specific independence. However, parameter estimation is often simpler under a direct parameterization, provided that the model enjoys certain decomposability properties. Here we introduce a cyclical projection algorithm for obtaining maximum likelihood estimates of log-linear parameters under an arbitrary context-specific graphical log-linear model, which needs not satisfy criteria of decomposability. We illustrate that lifting the restriction of decomposability makes the models more expressive, such that additional context-specific independencies embedded in real data can be identified. It is also shown how a context-specific graphical model can correspond to a non-hierarchical log-linear parameterization with a concise interpretation. This observation can pave way to further development of non-hierarchical log-linear models, which have been largely neglected due to their believed lack of interpretability.

As a well-known clustering algorithm, Fuzzy C-Means (FCM) allows each input sample to belong to more than one cluster, providing more flexibility than non-fuzzy clustering methods. However, the accuracy of FCM is subject to false detections caused by noisy records, weak feature selection and low certainty of the algorithm in some cases. The false detections are very important in some decision-making application domains like network security and medical diagnosis, where weak decisions based on such false detections may lead to catastrophic outcomes. They are mainly emerged from making decisions about a subset of records that do not provide enough evidence to make a good decision. In this paper, we propose a method for detecting such ambiguous records in FCM by introducing a certainty factor to decrease invalid detections. This approach enables us to send the detected ambiguous records to another discrimination method for a deeper investigation, thus increasing the accuracy by lowering the error rate. Most of the records are still processed quickly and with low error rate which prevents performance loss compared to similar hybrid methods. Experimental results of applying the proposed method on several datasets from different domains show a significant decrease in error rate as well as improved sensitivity of the algorithm.

Spectral clustering is a standard approach to label nodes on a graph by studying the (largest or lowest) eigenvalues of a symmetric real matrix such as e.g. the adjacency or the Laplacian. Recently, it has been argued that using instead a more complicated, non-symmetric and higher dimensional operator, related to the non-backtracking walk on the graph, leads to improved performance in detecting clusters, and even to optimal performance for the stochastic block model. Here, we propose to use instead a simpler object, a symmetric real matrix known as the Bethe Hessian operator, or deformed Laplacian. We show that this approach combines the performances of the non-backtracking operator, thus detecting clusters all the way down to the theoretical limit in the stochastic block model, with the computational, theoretical and memory advantages of real symmetric matrices.

The Gaussian process latent variable model (GP-LVM) provides a flexible approach for non-linear dimensionality reduction that has been widely applied. However, the current approach for training GP-LVMs is based on maximum likelihood, where the latent projection variables are maximized over rather than integrated out. In this paper we present a Bayesian method for training GP-LVMs by introducing a non-standard variational inference framework that allows to approximately integrate out the latent variables and subsequently train a GP-LVM by maximizing an analytic lower bound on the exact marginal likelihood. We apply this method for learning a GP-LVM from iid observations and for learning non-linear dynamical systems where the observations are temporally correlated. We show that a benefit of the variational Bayesian procedure is its robustness to overfitting and its ability to automatically select the dimensionality of the nonlinear latent space. The resulting framework is generic, flexible and easy to extend for other purposes, such as Gaussian process regression with uncertain inputs and semi-supervised Gaussian processes. We demonstrate our method on synthetic data and standard machine learning benchmarks, as well as challenging real world datasets, including high resolution video data.

Response calibration is the process of inferring how much the measured data depend on the signal one is interested in. It is essential for any quantitative signal estimation on the basis of the data. Here, we investigate self-calibration methods for linear signal measurements and linear dependence of the response on the calibration parameters. The common practice is to augment an external calibration solution using a known reference signal with an internal calibration on the unknown measurement signal itself. Contemporary self-calibration schemes try to find a self-consistent solution for signal and calibration by exploiting redundancies in the measurements. This can be understood in terms of maximizing the joint probability of signal and calibration. However, the full uncertainty structure of this joint probability around its maximum is thereby not taken into account by these schemes. Therefore better schemes -- in sense of minimal square error -- can be designed by accounting for asymmetries in the uncertainty of signal and calibration. We argue that at least a systematic correction of the common self-calibration scheme should be applied in many measurement situations in order to properly treat uncertainties of the signal on which one calibrates. Otherwise the calibration solutions suffer from a systematic bias, which consequently distorts the signal reconstruction. Furthermore, we argue that non-parametric, signal-to-noise filtered calibration should provide more accurate reconstructions than the common bin averages and provide a new, improved self-calibration scheme. We illustrate our findings with a simplistic numerical example.