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Anderson Crowder posted an update 6 months ago
In this paper, we consider prediction and variable selection in the misspecified binary classification models under the high-dimensional scenario. We focus on two approaches to classification, which are computationally efficient, but lead to model misspecification. The first one is to apply penalized logistic regression to the classification data, which possibly do not follow the logistic model. The second method is even more radical we just treat class labels of objects as they were numbers and apply penalized linear regression. In this paper, we investigate thoroughly these two approaches and provide conditions, which guarantee that they are successful in prediction and variable selection. Our results hold even if the number of predictors is much larger than the sample size. The paper is completed by the experimental results.The velocities of space plasma particles often follow kappa distribution functions, which have characteristic high energy tails. selleck kinase inhibitor The tails of these distributions are associated with low particle flux and, therefore, it is challenging to precisely resolve them in plasma measurements. On the other hand, the accurate determination of kappa distribution functions within a broad range of energies is crucial for the understanding of physical mechanisms. Standard analyses of the plasma observations determine the plasma bulk parameters from the statistical moments of the underlined distribution. It is important, however, to also quantify the uncertainties of the derived plasma bulk parameters, which determine the confidence level of scientific conclusions. We investigate the determination of the plasma bulk parameters from observations by an ideal electrostatic analyzer. We derive simple formulas to estimate the statistical uncertainties of the calculated bulk parameters. We then use the forward modelling method to simulate plasma observations by a typical top-hat electrostatic analyzer. We analyze the simulated observations in order to derive the plasma bulk parameters and their uncertainties. Our simulations validate our simplified formulas. We further examine the statistical errors of the plasma bulk parameters for several shapes of the plasma velocity distribution function.This paper uses quantitative eye tracking indicators to analyze the relationship between images of paintings and human viewing. First, we build the eye tracking fixation sequences through areas of interest (AOIs) into an information channel, the gaze channel. Although this channel can be interpreted as a generalization of a first-order Markov chain, we show that the gaze channel is fully independent of this interpretation, and stands even when first-order Markov chain modeling would no longer fit. The entropy of the equilibrium distribution and the conditional entropy of a Markov chain are extended with additional information-theoretic measures, such as joint entropy, mutual information, and conditional entropy of each area of interest. Then, the gaze information channel is applied to analyze a subset of Van Gogh paintings. Van Gogh artworks, classified by art critics into several periods, have been studied under computational aesthetics measures, which include the use of Kolmogorov complexity and permutation entropy. The gaze information channel paradigm allows the information-theoretic measures to analyze both individual gaze behavior and clustered behavior from observers and paintings. Finally, we show that there is a clear correlation between the gaze information channel quantities that come from direct human observation, and the computational aesthetics measures that do not rely on any human observation at all.Shape registration, finding the correct alignment of two sets of data, plays a significant role in computer vision such as objection recognition and image analysis. The iterative closest point (ICP) algorithm is one of well known and widely used algorithms in this area. The main purpose of this paper is to incorporate ICP with the fast convergent extended Hamiltonian learning (EHL), so called EHL-ICP algorithm, to perform planar and spatial rigid shape registration. By treating the registration error as the potential for the extended Hamiltonian system, the rigid shape registration is modelled as an optimization problem on the special Euclidean group S E ( n ) ( n = 2 , 3 ) . Our method is robust to initial values and parameters. Compared with some state-of-art methods, our approach shows better efficiency and accuracy by simulation experiments.Brain dynamics can exhibit narrow-band nonlinear oscillations and multistability. For a subset of disorders of consciousness and motor control, we hypothesized that some symptoms originate from the inability to spontaneously transition from one attractor to another. Using external perturbations, such as electrical pulses delivered by deep brain stimulation devices, it may be possible to induce such transition out of the pathological attractors. However, the induction of transition may be non-trivial, rendering the current open-loop stimulation strategies insufficient. In order to develop next-generation neural stimulators that can intelligently learn to induce attractor transitions, we require a platform to test the efficacy of such systems. To this end, we designed an analog circuit as a model for the multistable brain dynamics. The circuit spontaneously oscillates stably on two periods as an instantiation of a 3-dimensional continuous-time gated recurrent neural network. To discourage simple perturbation strategies, such as constant or random stimulation patterns from easily inducing transition between the stable limit cycles, we designed a state-dependent nonlinear circuit interface for external perturbation. We demonstrate the existence of nontrivial solutions to the transition problem in our circuit implementation.A restricted Boltzmann machine is a generative probabilistic graphic network. A probability of finding the network in a certain configuration is given by the Boltzmann distribution. Given training data, its learning is done by optimizing the parameters of the energy function of the network. In this paper, we analyze the training process of the restricted Boltzmann machine in the context of statistical physics. As an illustration, for small size bar-and-stripe patterns, we calculate thermodynamic quantities such as entropy, free energy, and internal energy as a function of the training epoch. We demonstrate the growth of the correlation between the visible and hidden layers via the subadditivity of entropies as the training proceeds. Using the Monte-Carlo simulation of trajectories of the visible and hidden vectors in the configuration space, we also calculate the distribution of the work done on the restricted Boltzmann machine by switching the parameters of the energy function. We discuss the Jarzynski equality which connects the path average of the exponential function of the work and the difference in free energies before and after training.
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