The quasi-Newton methods generally provide curvature information by approximating the Hessian using the secant equation. However, the secant equation becomes insipid in approximating the Newton step owing to its use of the first-order derivatives. In this study, we propose an approximate Newton step-based stochastic optimization algorithm for large-scale empirical risk minimization of convex functions with linear convergence rates. Specifically, we compute a partial column Hessian of size ($d\times k$) with $k\ll d$ randomly selected variables, then use the \textit{Nystr\"om method} to better approximate the full Hessian matrix. To further reduce the computational complexity per iteration, we directly compute the update step ($\Delta\boldsymbol{w}$) without computing and storing the full Hessian or its inverse. Furthermore, to address large-scale scenarios in which even computing a partial Hessian may require significant time, we used distribution-preserving (DP) sub-sampling to compute a partial Hessian. The DP sub-sampling generates $p$ sub-samples with similar first and second-order distribution statistics and selects a single sub-sample at each epoch in a round-robin manner to compute the partial Hessian. We integrate our approximated Hessian with stochastic gradient descent and stochastic variance-reduced gradients to solve the logistic regression problem. The numerical experiments show that the proposed approach was able to obtain a better approximation of Newton\textquotesingle s method with performance competitive with the state-of-the-art first-order and the stochastic quasi-Newton methods.

We consider the problem of high-dimensional Ising model selection using neighborhood-based least absolute shrinkage and selection operator (Lasso). It is rigorously proved that under some mild coherence conditions on the population covariance matrix of the Ising model, consistent model selection can be achieved with sample sizes $n=\Omega{(d^3\log{p})}$ for any tree-like graph in the paramagnetic phase, where $p$ is the number of variables and $d$ is the maximum node degree. When the same conditions are imposed directly on the sample covariance matrices, it is shown that a reduced sample size $n=\Omega{(d^2\log{p})}$ suffices. The obtained sufficient conditions for consistent model selection with Lasso are the same in the scaling of the sample complexity as that of $\ell_1$-regularized logistic regression. Given the popularity and efficiency of Lasso, our rigorous analysis provides a theoretical backing for its practical use in Ising model selection.

Figure 1 – Figure supplement 1: Learning curves on the random split-half validation used for model building. To facilitate comparisons, we evaluated predictions of age, fluid intelligence and neuroticism from a complete set of socio-demographic variables without brain imaging using the coefficient of determination R2 metric (y-axis) to compare results obtained from 100 to 3000 training samples (x-axis). The cross-validation (CV) distribution was obtained from 100 Monte Carlo splits. Across targets, performance started to plateau after around 1000 training samples with scores virtually identical to the final model used in subsequent analyses. These benchmarks suggest that inclusion of additional training samples would not have led to substantial improvements in performance.

In this paper, we introduce a reversible version of a genetically modified mode jumping Markov chain Monte Carlo algorithm (GMJMCMC) for inference on posterior model probabilities in complex model spaces, where the number of explanatory variables is prohibitively large for classical Markov Chain Monte Carlo methods. Unlike the earlier proposed GMJMCMC algorithm, the introduced algorithm is a proper MCMC and its limiting distribution corresponds to the posterior marginal model probabilities in the explored model space under reasonable regularity conditions.

We propose a nested weighted Tchebycheff Multi-objective Bayesian optimization framework where we build a regression model selection procedure from an ensemble of models, towards better estimation of the uncertain parameters of the weighted-Tchebycheff expensive black-box multi-objective function. In existing work, a weighted Tchebycheff MOBO approach has been demonstrated which attempts to estimate the unknown utopia in formulating acquisition function, through calibration using a priori selected regression model. However, the existing MOBO model lacks flexibility in selecting the appropriate regression models given the guided sampled data and therefore, can under-fit or over-fit as the iterations of the MOBO progress, reducing the overall MOBO performance. As it is too complex to a priori guarantee a best model in general, this motivates us to consider a portfolio of different families of predictive models fitted with current training data, guided by the WTB MOBO; the best model is selected following a user-defined prediction root mean-square-error-based approach. The proposed approach is implemented in optimizing a multi-modal benchmark problem and a thin tube design under constant loading of temperature-pressure, with minimizing the risk of creep-fatigue failure and design cost. Finally, the nested weighted Tchebycheff MOBO model performance is compared with different MOBO frameworks with respect to accuracy in parameter estimation, Pareto-optimal solutions and function evaluation cost. This method is generalized enough to consider different families of predictive models in the portfolio for best model selection, where the overall design architecture allows for solving any high-dimensional (multiple functions) complex black-box problems and can be extended to any other global criterion multi-objective optimization methods where prior knowledge of utopia is required.

Single-cell sequencing has a significant role to explore biological processes such as embryonic development, cancer evolution, and cell differentiation. These biological properties can be presented by a two-dimensional scatter plot. However, single-cell sequencing data generally has very high dimensionality. Therefore, dimensionality reduction should be used to process the high dimensional sequencing data for 2D visualization and subsequent biological analysis. The traditional dimensionality reduction methods, which do not consider the structure characteristics of single-cell sequencing data, are difficult to reveal the data structure in the 2D representation. In this paper, we develop a 2D feature representation method based on graph convolutional networks (GCN) for the visualization of single-cell data, termed single-cell sequencing graph embedding networks (SGEN). This method constructs the graph by the similarity relationship between cells and adopts GCN to analyze the neighbor embedding information of samples, which makes the similar cell closer to each other on the 2D scatter plot. The results show SGEN achieves obvious 2D distribution and preserves the high-dimensional relationship of different cells. Meanwhile, similar cell clusters have spatial continuity rather than relying heavily on random initialization, which can reflect the trajectory of cell development in this scatter plot.

Across all experiments, Hyperseed convincingly machine learning and robotics context is currently gaining a demonstrates its key novelties of learning from a few input great momentum [1]-[6]. In classification tasks, the use of vectors and single vector operation learning rule, both of which VSA leads to order of magnitude increase in energy efficiency contribute towards reduced time and computation complexity. of computations on the one hand and natively enables oneshot The paper is structured as follows. Section II describes and multitask learning on the other [7]. It is prospected the related work relevant to Hyperseed operations. The used that VSA will play a key role in the development of novel methods including the fundamentals of VSA are presented neuromorphic computer architectures [8] as an algorithmic in Section III. Section IV presents the main contribution - abstraction [9], [10]. The main contribution of this paper is the method for unsupervised learning Hyperseed. Section V a novel algorithm for unsupervised learning called Hyperseed, reports the results of the performance evaluation the experiments.

In the last few years, Deep Learning models have become increasingly popular. However, their deployment is still precluded in those contexts where the amount of supervised data is limited and manual labelling expensive. Active learning strategies aim at solving this problem by requiring supervision only on few unlabelled samples, which improve the most model performances after adding them to the training set. Most strategies are based on uncertain sample selection, and even often restricted to samples lying close to the decision boundary. Here we propose a very different approach, taking into consideration domain knowledge. Indeed, in the case of multi-label classification, the relationships among classes offer a way to spot incoherent predictions, i.e., predictions where the model may most likely need supervision. We have developed a framework where first-order-logic knowledge is converted into constraints and their violation is checked as a natural guide for sample selection. We empirically demonstrate that knowledge-driven strategy outperforms standard strategies, particularly on those datasets where domain knowledge is complete. Furthermore, we show how the proposed approach enables discovering data distributions lying far from training data. Finally, the proposed knowledge-driven strategy can be also easily used in object-detection problems where standard uncertainty-based techniques are difficult to apply.

Clinical characterization and interpretation of respiratory sound symptoms have remained a challenge due to the similarities in the audio properties that manifest during auscultation in medical diagnosis. The misinterpretation and conflation of these sounds coupled with the comorbidity cases of the associated ailments - particularly, exercised-induced respiratory conditions; result in the under-diagnosis and undertreatment of the conditions. Though several studies have proposed computerized systems for objective classification and evaluation of these sounds, most of the algorithms run on desktop and backend systems. In this study, we leverage the improved computational and storage capabilities of modern smartphones to distinguish the respiratory sound symptoms using machine learning algorithms namely: Random Forest (RF), Support Vector Machine (SVM), and k-Nearest Neighbour (k-NN). The appreciable performance of these classifiers on a mobile phone shows smartphone as an alternate tool for recognition and discrimination of respiratory symptoms in real-time scenarios. Further, the objective clinical data provided by the machine learning process could aid physicians in the screening and treatment of a patient during ambulatory care where specialized medical devices may not be readily available.

Extreme events with potential deadly outcomes, such as those organized by terror groups, are highly unpredictable in nature and an imminent threat to society. In particular, quantifying the likelihood of a terror attack occurring in an arbitrary space-time region and its relative societal risk, would facilitate informed measures that would strengthen national security. This paper introduces a novel self-exciting marked spatio-temporal model for attacks whose inhomogeneous baseline intensity is written as a function of covariates. Its triggering intensity is succinctly modeled with a Gaussian Process prior distribution to flexibly capture intricate spatio-temporal dependencies between an arbitrary attack and previous terror events. By inferring the parameters of this model, we highlight specific space-time areas in which attacks are likely to occur. Furthermore, by measuring the outcome of an attack in terms of the number of casualties it produces, we introduce a novel mixture distribution for the number of casualties. This distribution flexibly handles low and high number of casualties and the discrete nature of the data through a {\it Generalized ZipF} distribution. We rely on a customized Markov chain Monte Carlo (MCMC) method to estimate the model parameters. We illustrate the methodology with data from the open source Global Terrorism Database (GTD) that correspond to attacks in Afghanistan from 2013-2018. We show that our model is able to predict the intensity of future attacks for 2019-2021 while considering various covariates of interest such as population density, number of regional languages spoken, and the density of population supporting the opposing government.