Unsupervised learning of human motion

An unsupervised learning algorithm that can obtain a probabilistic model of an object composed of a collection of parts (a moving human body in our examples) automatically from unlabeled training data is presented. The training data include both useful "foreground" features as well as features that arise from irrelevant background clutter - the correspondence between parts and detected features is unknown. The joint probability density function of the parts is represented by a mixture of decomposable triangulated graphs which allow for fast detection. To learn the model structure as well as model parameters, an EM-like algorithm is developed where the labeling of the data (part assignments) is treated as hidden variables. The unsupervised learning technique is not limited to decomposable triangulated graphs. The efficiency and effectiveness of our algorithm is demonstrated by applying it to generate models of human motion automatically from unlabeled image sequences, and testing the learned models on a variety of sequences

Detecting positive correlations in a multivariate sample

We consider the problem of testing whether a correlation matrix of a multivariate normal population is the identity matrix. We focus on sparse classes of alternatives where only a few entries are nonzero and, in fact, positive. We derive a general lower bound applicable to various classes and study the performance of some near-optimal tests. We pay special attention to computational feasibility and construct near-optimal tests that can be computed efficiently. Finally, we apply our results to prove new lower bounds for the clique number of high-dimensional random geometric graphs.Comment: Published at http://dx.doi.org/10.3150/13-BEJ565 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Future Detection of Supernova Neutrino Burst and Explosion Mechanism

Future detection of a supernova neutrino burst by large underground detectors would give important information for the explosion mechanism of collapse-driven supernovae. We studied the statistical analysis for the future detection of a nearby supernova by using a numerical supernova model and realistic Monte-Carlo simulations of detection by the Super-Kamiokande detector. We mainly discuss the detectability of the signatures of the delayed explosion mechanism in the time evolution of the \anue luminosity and spectrum. For a supernova at 10 kpc away from the Earth, we find that not only the signature is clearly discernible, but also the deviation of energy spectrum from the Fermi-Dirac (FD) distribution can be observed. The deviation from the FD distribution would, if observed, provide a test for the standard picture of neutrino emission from collapse-driven supernovae. For the $D$ = 50 kpc case, the signature of the delayed explosion is still observable, but statistical fluctuation is too large to detect the deviation from the FD distribution. We also propose a method for statistical reconstruction of the time evolution of \anue luminosity and spectrum from data, by which we can get a smoother time evolution and smaller statistical errors than a simple, time-binning analysis. This method is useful especially when the available number of events is relatively small, e.g., a supernova in the LMC or SMC. Neutronization burst of $\nu_e$'s produces about 5 scattering events when $D$ = 10 kpc and this signal is difficult to distinguish from \anue p events.Comment: 28 pages including all figures. Accepted by Astrophys.

Stochastic Digital Backpropagation with Residual Memory Compensation

Stochastic digital backpropagation (SDBP) is an extension of digital backpropagation (DBP) and is based on the maximum a posteriori principle. SDBP takes into account noise from the optical amplifiers in addition to handling deterministic linear and nonlinear impairments. The decisions in SDBP are taken on a symbol-by-symbol (SBS) basis, ignoring any residual memory, which may be present due to non-optimal processing in SDBP. In this paper, we extend SDBP to account for memory between symbols. In particular, two different methods are proposed: a Viterbi algorithm (VA) and a decision directed approach. Symbol error rate (SER) for memory-based SDBP is significantly lower than the previously proposed SBS-SDBP. For inline dispersion-managed links, the VA-SDBP has up to 10 and 14 times lower SER than DBP for QPSK and 16-QAM, respectively.Comment: 7 pages, accepted to publication in 'Journal of Lightwave Technology (JLT)

Lower Bounds for Two-Sample Structural Change Detection in Ising and Gaussian Models

The change detection problem is to determine if the Markov network structures of two Markov random fields differ from one another given two sets of samples drawn from the respective underlying distributions. We study the trade-off between the sample sizes and the reliability of change detection, measured as a minimax risk, for the important cases of the Ising models and the Gaussian Markov random fields restricted to the models which have network structures with $p$ nodes and degree at most $d$, and obtain information-theoretic lower bounds for reliable change detection over these models. We show that for the Ising model, $\Omega\left(\frac{d^2}{(\log d)^2}\log p\right)$ samples are required from each dataset to detect even the sparsest possible changes, and that for the Gaussian, $\Omega\left( \gamma^{-2} \log(p)\right)$ samples are required from each dataset to detect change, where $\gamma$ is the smallest ratio of off-diagonal to diagonal terms in the precision matrices of the distributions. These bounds are compared to the corresponding results in structure learning, and closely match them under mild conditions on the model parameters. Thus, our change detection bounds inherit partial tightness from the structure learning schemes in previous literature, demonstrating that in certain parameter regimes, the naive structure learning based approach to change detection is minimax optimal up to constant factors.Comment: Presented at the 55th Annual Allerton Conference on Communication, Control, and Computing, Oct. 201

Probing many-body dynamics on a 51-atom quantum simulator

Controllable, coherent many-body systems can provide insights into the fundamental properties of quantum matter, enable the realization of new quantum phases and could ultimately lead to computational systems that outperform existing computers based on classical approaches. Here we demonstrate a method for creating controlled many-body quantum matter that combines deterministically prepared, reconfigurable arrays of individually trapped cold atoms with strong, coherent interactions enabled by excitation to Rydberg states. We realize a programmable Ising-type quantum spin model with tunable interactions and system sizes of up to 51 qubits. Within this model, we observe phase transitions into spatially ordered states that break various discrete symmetries, verify the high-fidelity preparation of these states and investigate the dynamics across the phase transition in large arrays of atoms. In particular, we observe robust manybody dynamics corresponding to persistent oscillations of the order after a rapid quantum quench that results from a sudden transition across the phase boundary. Our method provides a way of exploring many-body phenomena on a programmable quantum simulator and could enable realizations of new quantum algorithms.Comment: 17 pages, 13 figure