Local competition among neighboring neurons is a common procedure taking place in biological systems. This finding has inspired research on more biologically plausible deep networks that comprise competing linear units, as opposed to nonlinear units that do not entail any form of (local) competition. This paper revisits this modeling paradigm, with the aim of enabling inference of networks that retain state-of-the-art accuracy for the least possible model complexity; this includes the needed number of connections or locally competing sets of units, as well as the required floating-point precision for storing the network weights. To this end, we leverage solid arguments from the field of Bayesian nonparametrics. Specifically, we introduce auxiliary discrete latent variables of model component utility, and perform Bayesian inference over them. Then, we impose appropriate stick-breaking priors over the introduced discrete latent variables; these give rise to a well-established sparsity-inducing mechanism. As we experimentally show using benchmark datasets, our approach yields networks with less memory footprint than the state-of-the-art, and with no compromises in predictive accuracy.

We apply the Ordered Weighted Averaging (OWA) operator in multi-criteria decision-making. To satisfy different kinds of uncertainty, measure based dominance has been presented to gain the order of different criterion. However, this idea has not been applied in fuzzy system until now. In this paper, we focus on the situation where the linguistic satisfactions are fuzzy measures instead of the exact values. We review the concept of OWA operator and discuss the order mechanism of fuzzy number. Then we combine with measure-based dominance to give an overall score of each alternatives. An example is illustrated to show the whole procedure.

The region of heavy calcium isotopes forms the frontier of experimental and theoretical nuclear structure research where the basic concepts of nuclear physics are put to stringent test. The recent discovery of the extremely neutron-rich nuclei around $^{60}$Ca [Tarasov, 2018] and the experimental determination of masses for $^{55-57}$Ca (Michimasa, 2018] provide unique information about the binding energy surface in this region. To assess the impact of these experimental discoveries on the nuclear landscape's extent, we use global mass models and statistical machine learning to make predictions, with quantified levels of certainty, for bound nuclides between Si and Ti. Using a Bayesian model averaging analysis based on Gaussian-process-based extrapolations we introduce the posterior probability $p_{ex}$ for each nucleus to be bound to neutron emission. We find that extrapolations for drip-line locations, at which the nuclear binding ends, are consistent across the global mass models used, in spite of significant variations between their raw predictions. In particular, considering the current experimental information and current global mass models, we predict that $^{68}$Ca has an average posterior probability ${p_{ex}\approx76}$% to be bound to two-neutron emission while the nucleus $^{61}$Ca is likely to decay by emitting a neutron (${p_{ex}\approx 46}$ %).

We introduce a new framework for estimating the support size of an unknown distribution which improves upon known approximation-based techniques. Our main contributions include describing a rigorous new weighted Chebyshev polynomial approximation method and introducing regularization terms into the problem formulation that provably improve the performance of state-of-the-art approximation-based approaches. In particular, we present both theoretical and computer simulation results that illustrate the utility and performance improvements of our method. The theoretical analysis relies on jointly optimizing the bias and variance components of the risk, and combining new weighted minmax polynomial approximation techniques with discretized semi-infinite programming solvers. Such a setting allows for casting the estimation problem as a linear program (LP) with a small number of variables and constraints that may be solved as efficiently as the original Chebyshev approximation-based problem. The described approach also applies to the support coverage and entropy estimation problems. Our newly developed technique is tested on synthetic data and used to estimate the number of bacterial species in the human gut. On synthetic datasets, we observed up to five-fold improvements in the value of the worst-case risk. For the bioinformatics application, metagenomic data from the NIH Human Gut and the American Gut Microbiome was combined and processed to obtain lists of bacterial taxonomies. These were subsequently used to compute the bacterial species histograms and estimate the number of bacterial species in the human gut to roughly 2350, with the species being represented by trillions of cells.

Many time-series data including text, movies, and biological signals can be represented as sequences of correlated binary patterns. These patterns may be described by weighted combinations of a few dominant structures that underpin specific interactions among the binary elements. To extract the dominant correlation structures and their contributions to generating data in a time-dependent manner, we model the dynamics of binary patterns using the state-space model of an Ising-type network that is composed of multiple undirected graphs. We provide a sequential Bayes algorithm to estimate the dynamics of weights on the graphs while gaining the graph structures online. This model can uncover overlapping graphs underlying the data better than a traditional orthogonal decomposition method, and outperforms an original time-dependent full Ising model. We assess the performance of the method by simulated data, and demonstrate that spontaneous activity of cultured hippocampal neurons is represented by dynamics of multiple graphs.

We propose a fast, simple and robust algorithm for computing shortest paths and distances on Riemannian manifolds learned from data. This amounts to solving a system of ordinary differential equations (ODEs) subject to boundary conditions. Here standard solvers perform poorly because they require well-behaved Jacobians of the ODE, and usually, manifolds learned from data imply unstable and ill-conditioned Jacobians. Instead, we propose a fixed-point iteration scheme for solving the ODE that avoids Jacobians. This enhances the stability of the solver, while reduces the computational cost. In experiments involving both Riemannian metric learning and deep generative models we demonstrate significant improvements in speed and stability over both general-purpose state-of-the-art solvers as well as over specialized solvers.

Algorithms are the smart and powerful soldier of a complex machine learning model. In other words, machine learning algorithms are the core foundation when we play with data or when it's come to training the model. In this article, you and I are going on a tour called "7 major machine learning algorithms and their application " The purpose of this tour is to either brush up the mind or to gain an essential understanding of machine learning algorithm. We will find the major answer in this tour like for what purpose machine learning algorithms works, where to use them, when to use them and how to use them. Before getting deeper let's have a brief introduction. Machine learning algorithms are mainly classified into 3 broad categories i.e supervised learning, unsupervised learning, and reinforcement learning. In supervised learning machine learning algorithms, the machine is taught by example. Here the operator provides the machine learning algorithm with the dataset. This dataset includes desired inputs and outputs variables. By the use of these set of variables, we generate a function that map inputs to desired outputs.

Label shift refers to the phenomenon where the marginal probability p(y) of observing a particular class changes between the training and test distributions while the conditional probability p(x|y) stays fixed. This is relevant in settings such as medical diagnosis, where a classifier trained to predict disease based on observed symptoms may need to be adapted to a different distribution where the baseline frequency of the disease is higher. Given calibrated estimates of p(y|x), one can apply an EM algorithm to correct for the shift in class imbalance between the training and test distributions without ever needing to calculate p(x|y). Unfortunately, modern neural networks typically fail to produce well-calibrated probabilities, compromising the effectiveness of this approach. Although Temperature Scaling can greatly reduce miscalibration in these networks, it can leave behind a systematic bias in the probabilities that still poses a problem. To address this, we extend Temperature Scaling with class-specific bias parameters, which largely eliminates systematic bias in the calibrated probabilities and allows for effective domain adaptation under label shift. We term our calibration approach "Bias-Corrected Temperature Scaling". On experiments with CIFAR10, we find that EM with Bias-Corrected Temperature Scaling significantly outperforms both EM with Temperature Scaling and the recently-proposed Black-Box Shift Estimation.

This paper is a step-by-step tutorial for fitting a mixture distribution to data. It merely assumes the reader has the background of calculus and linear algebra. Other required background is briefly reviewed before explaining the main algorithm. In explaining the main algorithm, first, fitting a mixture of two distributions is detailed and examples of fitting two Gaussians and Poissons, respectively for continuous and discrete cases, are introduced. Thereafter, fitting several distributions in general case is explained and examples of several Gaussians (Gaussian Mixture Model) and Poissons are again provided. Model-based clustering, as one of the applications of mixture distributions, is also introduced. Numerical simulations are also provided for both Gaussian and Poisson examples for the sake of better clarification.

Machine learning is using data we have (known as training data) to learn a function that we can use to make predictions about data we don't have yet. The simplest example of this is linear regression, where we learn the slope and intercept of a line so we can predict the vertical position of points from their horizontal position. This is shown below, the training data are the blue points and the learnt function is the red line. Machine learning is an extension of linear regression in a few ways. Secondly, modern ML uses much more powerful methods for extracting patterns of which deep learning is only one of many.