Learning with a mutualistic teacher

The concept of a “mutualistic teacher” is introduced for unsupervised learning of the mean vectors of the components of a mixture of multivariate normal densities, when the number of classes is also unknown. The unsupervised learning problem is formulated here as a multi-stage quasi-supervised problem incorporating a cluster approach. The mutualistic teacher creates a quasi-supervised environment at each stage by picking out “mutual pairs” of samples and assigning identical (but unknown) labels to the individuals of each mutual pair. The number of classes, if not specified, can be determined at an intermediate stage. The risk in assigning identical labels to the individuals of mutual pairs is estimated. Results of some simulation studies are presented.

Predictive uncertainty of chaotic daily streamflow using ensemble wavelet networks approach

Perfect or even mediocre weather predictions over a long period are almost impossible because of the ultimate growth of a small initial error into a significant one. Even though the sensitivity of initial conditions limits the predictability in chaotic systems, an ensemble of prediction from different possible initial conditions and also a prediction algorithm capable of resolving the fine structure of the chaotic attractor can reduce the prediction uncertainty to some extent. All of the traditional chaotic prediction methods in hydrology are based on single optimum initial condition local models which can model the sudden divergence of the trajectories with different local functions. Conceptually, global models are ineffective in modeling the highly unstable structure of the chaotic attractor. This paper focuses on an ensemble prediction approach by reconstructing the phase space using different combinations of chaotic parameters, i.e., embedding dimension and delay time to quantify the uncertainty in initial conditions. The ensemble approach is implemented through a local learning wavelet network model with a global feed-forward neural network structure for the phase space prediction of chaotic streamflow series. Quantification of uncertainties in future predictions are done by creating an ensemble of predictions with wavelet network using a range of plausible embedding dimensions and delay times. The ensemble approach is proved to be 50% more efficient than the single prediction for both local approximation and wavelet network approaches. The wavelet network approach has proved to be 30%-50% more superior to the local approximation approach. Compared to the traditional local approximation approach with single initial condition, the total predictive uncertainty in the streamflow is reduced when modeled with ensemble wavelet networks for different lead times. Localization property of wavelets, utilizing different dilation and translation parameters, helps in capturing most of the statistical properties of the observed data. The need for taking into account all plausible initial conditions and also bringing together the characteristics of both local and global approaches to model the unstable yet ordered chaotic attractor of a hydrologic series is clearly demonstrated.

A Coordinated Interdependent Protein Circuitry Stabilizes the Kinetochore Ensemble to Protect CENP-A in the Human Pathogenic Yeast Candida albicans

Unlike most eukaryotes, a kinetochore is fully assembled early in the cell cycle in budding yeasts Saccharomyces cerevisiae and Candida albicans. These kinetochores are clustered together throughout the cell cycle. Kinetochore assembly on point centromeres of S. cerevisiae is considered to be a step-wise process that initiates with binding of inner kinetochore proteins on specific centromere DNA sequence motifs. In contrast, kinetochore formation in C. albicans, that carries regional centromeres of 3-5 kb long, has been shown to be a sequence independent but an epigenetically regulated event. In this study, we investigated the process of kinetochore assembly/disassembly in C. albicans. Localization dependence of various kinetochore proteins studied by confocal microscopy and chromatin immunoprecipitation (ChIP) assays revealed that assembly of a kinetochore is a highly coordinated and interdependent event. Partial depletion of an essential kinetochore protein affects integrity of the kinetochore cluster. Further protein depletion results in complete collapse of the kinetochore architecture. In addition, GFP-tagged kinetochore proteins confirmed similar time-dependent disintegration upon gradual depletion of an outer kinetochore protein (Dam1). The loss of integrity of a kinetochore formed on centromeric chromatin was demonstrated by reduced binding of CENP-A and CENP-C at the centromeres. Most strikingly, Western blot analysis revealed that gradual depletion of any of these essential kinetochore proteins results in concomitant reduction in cellular protein levels of CENP-A. We further demonstrated that centromere bound CENP-A is protected from the proteosomal mediated degradation. Based on these results, we propose that a coordinated interdependent circuitry of several evolutionarily conserved essential kinetochore proteins ensures integrity of a kinetochore formed on the foundation of CENP-A containing centromeric chromatin.

NESTED SPARSE BAYESIAN LEARNING FOR BLOCK-SPARSE SIGNALS WITH INTRA-BLOCK CORRELATION

In this work, we address the recovery of block sparse vectors with intra-block correlation, i.e., the recovery of vectors in which the correlated nonzero entries are constrained to lie in a few clusters, from noisy underdetermined linear measurements. Among Bayesian sparse recovery techniques, the cluster Sparse Bayesian Learning (SBL) is an efficient tool for block-sparse vector recovery, with intra-block correlation. However, this technique uses a heuristic method to estimate the intra-block correlation. In this paper, we propose the Nested SBL (NSBL) algorithm, which we derive using a novel Bayesian formulation that facilitates the use of the monotonically convergent nested Expectation Maximization (EM) and a Kalman filtering based learning framework. Unlike the cluster-SBL algorithm, this formulation leads to closed-form EMupdates for estimating the correlation coefficient. We demonstrate the efficacy of the proposed NSBL algorithm using Monte Carlo simulations.

A Split-and-Merge Dictionary Learning Algorithm for Sparse Representation: Application to Image Denoising

In big data image/video analytics, we encounter the problem of learning an over-complete dictionary for sparse representation from a large training dataset, which cannot be processed at once because of storage and computational constraints. To tackle the problem of dictionary learning in such scenarios, we propose an algorithm that exploits the inherent clustered structure of the training data and make use of a divide-and-conquer approach. The fundamental idea behind the algorithm is to partition the training dataset into smaller clusters, and learn local dictionaries for each cluster. Subsequently, the local dictionaries are merged to form a global dictionary. Merging is done by solving another dictionary learning problem on the atoms of the locally trained dictionaries. This algorithm is referred to as the split-and-merge algorithm. We show that the proposed algorithm is efficient in its usage of memory and computational complexity, and performs on par with the standard learning strategy, which operates on the entire data at a time. As an application, we consider the problem of image denoising. We present a comparative analysis of our algorithm with the standard learning techniques that use the entire database at a time, in terms of training and denoising performance. We observe that the split-and-merge algorithm results in a remarkable reduction of training time, without significantly affecting the denoising performance.

Joint Channel Estimation and Data Detection in MIMO-OFDM Systems: A Sparse Bayesian Learning Approach

The impulse response of wireless channels between the N-t transmit and N-r receive antennas of a MIMO-OFDM system are group approximately sparse (ga-sparse), i.e., NtNt the channels have a small number of significant paths relative to the channel delay spread and the time-lags of the significant paths between transmit and receive antenna pairs coincide. Often, wireless channels are also group approximately cluster-sparse (gac-sparse), i.e., every ga-sparse channel consists of clusters, where a few clusters have all strong components while most clusters have all weak components. In this paper, we cast the problem of estimating the ga-sparse and gac-sparse block-fading and time-varying channels in the sparse Bayesian learning (SBL) framework and propose a bouquet of novel algorithms for pilot-based channel estimation, and joint channel estimation and data detection, in MIMO-OFDM systems. The proposed algorithms are capable of estimating the sparse wireless channels even when the measurement matrix is only partially known. Further, we employ a first-order autoregressive modeling of the temporal variation of the ga-sparse and gac-sparse channels and propose a recursive Kalman filtering and smoothing (KFS) technique for joint channel estimation, tracking, and data detection. We also propose novel, parallel-implementation based, low-complexity techniques for estimating gac-sparse channels. Monte Carlo simulations illustrate the benefit of exploiting the gac-sparse structure in the wireless channel in terms of the mean square error (MSE) and coded bit error rate (BER) performance.