Dynamic networks are a general language for describing time-evolving complex systems, and discrete time network models provide an emerging statistical technique for various applications. It is a fundamental research question to detect the community structure in time-evolving networks. However, due to significant computational challenges and difficulties in modeling communities of time-evolving networks, there is little progress in the current literature to effectively find communities in time-evolving networks. In this work, we propose a novel model-based clustering framework for time-evolving networks based on discrete time exponential-family random graph models. To choose the number of communities, we use conditional likelihood to construct an effective model selection criterion. Furthermore, we propose an efficient variational expectation-maximization (EM) algorithm to find approximate maximum likelihood estimates of network parameters and mixing proportions. By using variational methods and minorization-maximization (MM) techniques, our method has appealing scalability for large-scale time-evolving networks. The power of our method is demonstrated in simulation studies and empirical applications to international trade networks and the collaboration networks of a large American research university.

Monte Carlo methods are essential tools for Bayesian inference. Gibbs sampling is a well-known Markov chain Monte Carlo (MCMC) algorithm, extensively used in signal processing, machine learning, and statistics, employed to draw samples from complicated high-dimensional posterior distributions. The key point for the successful application of the Gibbs sampler is the ability to draw efficiently samples from the full-conditional probability density functions. Since in the general case this is not possible, in order to speed up the convergence of the chain, it is required to generate auxiliary samples whose information is eventually disregarded. In this work, we show that these auxiliary samples can be recycled within the Gibbs estimators, improving their efficiency with no extra cost. This novel scheme arises naturally after pointing out the relationship between the standard Gibbs sampler and the chain rule used for sampling purposes. Numerical simulations involving simple and real inference problems confirm the excellent performance of the proposed scheme in terms of accuracy and computational efficiency. In particular we give empirical evidence of performance in a toy example, inference of Gaussian processes hyperparameters, and learning dependence graphs through regression.

Convolutional Neural Network is known as ConvNet have been extensively used in many complex machine learning tasks. However, hyperparameters optimization is one of a crucial step in developing ConvNet architectures, since the accuracy and performance are totally reliant on the hyperparameters. This multilayered architecture parameterized by a set of hyperparameters such as the number of convolutional layers, number of fully connected dense layers & neurons, the probability of dropout implementation, learning rate. Hence the searching the hyperparameter over the hyperparameter space are highly difficult to build such complex hierarchical architecture. Many methods have been proposed over the decade to explore the hyperparameter space and find the optimum set of hyperparameter values. Reportedly, Gird search and Random search are said to be inefficient and extremely expensive, due to a large number of hyperparameters of the architecture. Hence, Sequential model-based Bayesian Optimization is a promising alternative technique to address the extreme of the unknown cost function. The recent study on Bayesian Optimization by Snoek in nine convolutional network parameters is achieved the lowerest error report in the CIFAR-10 benchmark. This article is intended to provide the overview of the mathematical concept behind the Bayesian Optimization over a Gaussian prior.

We propose an efficient algorithm for approximate computation of the profile maximum likelihood (PML), a variant of maximum likelihood maximizing the probability of observing a sufficient statistic rather than the empirical sample. The PML has appealing theoretical properties, but is difficult to compute exactly. Inspired by observations gleaned from exactly solvable cases, we look for an approximate PML solution, which, intuitively, clumps comparably frequent symbols into one symbol. This amounts to lower-bounding a certain matrix permanent by summing over a subgroup of the symmetric group rather than the whole group during the computation. We extensively experiment with the approximate solution, and find the empirical performance of our approach is competitive and sometimes significantly better than state-of-the-art performance for various estimation problems.

In this paper we develop a method for learning nonlinear systems with multiple outputs and inputs. We begin by modelling the errors of a nominal predictor of the system using a latent variable framework. Then using the maximum likelihood principle we derive a criterion for learning the model. The resulting optimization problem is tackled using a majorization-minimization approach. Finally, we develop a convex majorization technique and show that it enables a recursive identification method. The method learns parsimonious predictive models and is tested on both synthetic and real nonlinear systems.

Optimization results are one method for understanding neural computation from Nature's perspective and for defining the physical limits on neuron-like engineering. Earlier work looks at individual properties or performance criteria and occasionally a combination of two, such as energy and information. Here we make use of Jaynes' maximum entropy method and combine a larger set of constraints, possibly dimensionally distinct, each expressible as an expectation. The method identifies a likelihood-function and a sufficient statistic arising from each such optimization. This likelihood is a first-hitting time distribution in the exponential class. Particular constraint sets are identified that, from an optimal inference perspective, justify earlier neurocomputational models. Interactions between constraints, mediated through the inferred likelihood, restrict constraint-set parameterizations, e.g., the energy-budget limits estimation performance which, in turn, matches an axonal communication constraint. Such linkages are, for biologists, experimental predictions of the method. In addition to the related likelihood, at least one type of constraint set implies marginal distributions, and in this case, a Shannon bits/joule statement arises.

The functions of proteins and RNAs are determined by a myriad of interactions between their constituent residues, but most quantitative models of how molecular phenotype depends on genotype must approximate this by simple additive effects. While recent models have relaxed this constraint to also account for pairwise interactions, these approaches do not provide a tractable path towards modeling higher-order dependencies. Here, we show how latent variable models with nonlinear dependencies can be applied to capture beyond-pairwise constraints in biomolecules. We present a new probabilistic model for sequence families, DeepSequence, that can predict the effects of mutations across a variety of deep mutational scanning experiments significantly better than site independent or pairwise models that are based on the same evolutionary data. The model, learned in an unsupervised manner solely from sequence information, is grounded with biologically motivated priors, reveals latent organization of sequence families, and can be used to extrapolate to new parts of sequence space.

The bag of words (BOW) represents a corpus in a matrix whose elements are the frequency of words. However, each row in the matrix is a very high-dimensional sparse vector. Dimension reduction (DR) is a popular method to address sparsity and high-dimensionality issues. Among different strategies to develop DR method, Unsupervised Feature Transformation (UFT) is a popular strategy to map all words on a new basis to represent BOW. The recent increase of text data and its challenges imply that DR area still needs new perspectives. Although a wide range of methods based on the UFT strategy has been developed, the fuzzy approach has not been considered for DR based on this strategy. This research investigates the application of fuzzy clustering as a DR method based on the UFT strategy to collapse BOW matrix to provide a lower-dimensional representation of documents instead of the words in a corpus. The quantitative evaluation shows that fuzzy clustering produces superior performance and features to Principal Components Analysis (PCA) and Singular Value Decomposition (SVD), two popular DR methods based on the UFT strategy.

Critical to evaluating the capacity, scalability, and availability of web systems are realistic web traffic generators. Web traffic generation is a classic research problem, no generator accounts for the characteristics of web robots or crawlers that are now the dominant source of traffic to a web server. Administrators are thus unable to test, stress, and evaluate how their systems perform in the face of ever increasing levels of web robot traffic. To resolve this problem, this paper introduces a novel approach to generate synthetic web robot traffic with high fidelity. It generates traffic that accounts for both the temporal and behavioral qualities of robot traffic by statistical and Bayesian models that are fitted to the properties of robot traffic seen in web logs from North America and Europe. We evaluate our traffic generator by comparing the characteristics of generated traffic to those of the original data. We look at session arrival rates, inter-arrival times and session lengths, comparing and contrasting them between generated and real traffic. Finally, we show that our generated traffic affects cache performance similarly to actual traffic, using the common LRU and LFU eviction policies.