Robust computation of linear models by convex relaxation

Consider a dataset of vector-valued observations that consists of noisy inliers, which are explained well by a low-dimensional subspace, along with some number of outliers. This work describes a convex optimization problem, called REAPER, that can reliably fit a low-dimensional model to this type of data. This approach parameterizes linear subspaces using orthogonal projectors, and it uses a relaxation of the set of orthogonal projectors to reach the convex formulation. The paper provides an efficient algorithm for solving the REAPER problem, and it documents numerical experiments which confirm that REAPER can dependably find linear structure in synthetic and natural data. In addition, when the inliers lie near a low-dimensional subspace, there is a rigorous theory that describes when REAPER can approximate this subspace.Comment: Formerly titled "Robust computation of linear models, or How to find a needle in a haystack

Accelerated Parallel Non-conjugate Sampling for Bayesian Non-parametric Models

Inference of latent feature models in the Bayesian nonparametric setting is generally difficult, especially in high dimensional settings, because it usually requires proposing features from some prior distribution. In special cases, where the integration is tractable, we could sample new feature assignments according to a predictive likelihood. However, this still may not be efficient in high dimensions. We present a novel method to accelerate the mixing of latent variable model inference by proposing feature locations from the data, as opposed to the prior. First, we introduce our accelerated feature proposal mechanism that we will show is a valid Bayesian inference algorithm and next we propose an approximate inference strategy to perform accelerated inference in parallel. This sampling method is efficient for proper mixing of the Markov chain Monte Carlo sampler, computationally attractive, and is theoretically guaranteed to converge to the posterior distribution as its limiting distribution.Comment: Previously known as "Accelerated Inference for Latent Variable Models

Theory for supersolid 4^4He

Although both vacancies and interstitial have relatively high activation energies in the normal solid, we propose that a lower energy bound state of a vacancy and an interstitial may facilitate vacancy condensation to give supersolidity in $^{4}$He . We use a phenomenological two-band boson lattice model to demonstrate this new mechanism and discuss the possible relevance to the recently observed superfluid-like, non-classical rotational inertial experiments of Kim and Chan in solid $^{4}$He. Some of our results may also be applicable to trapped bosons in optical lattices.Comment: 5 pages, 2 figure

Sequential Gaussian Processes for Online Learning of Nonstationary Functions

Many machine learning problems can be framed in the context of estimating functions, and often these are time-dependent functions that are estimated in real-time as observations arrive. Gaussian processes (GPs) are an attractive choice for modeling real-valued nonlinear functions due to their flexibility and uncertainty quantification. However, the typical GP regression model suffers from several drawbacks: i) Conventional GP inference scales $O(N^{3})$ with respect to the number of observations; ii) updating a GP model sequentially is not trivial; and iii) covariance kernels often enforce stationarity constraints on the function, while GPs with non-stationary covariance kernels are often intractable to use in practice. To overcome these issues, we propose an online sequential Monte Carlo algorithm to fit mixtures of GPs that capture non-stationary behavior while allowing for fast, distributed inference. By formulating hyperparameter optimization as a multi-armed bandit problem, we accelerate mixing for real time inference. Our approach empirically improves performance over state-of-the-art methods for online GP estimation in the context of prediction for simulated non-stationary data and hospital time series data

Structures of K0.05Na0.95NbO3 (50–300 K) and K0.30Na0.70NbO3 (100–200 K)

Rietveld refinement using neutron powder diffraction data is reported for the potential lead-free piezoelectric material KxNa1 - xNbO3 (x = 0.05, x = 0.3) at low temperatures. The structures were determined to be of rhombohedral symmetry, space group R3c, with the tilt system a-a-a- for both compositions. It was found that some of the structural parameters differ significantly in the two structures, and particularly the NbO6 octahedral strains as a function of temperature. The 300 K profile for K0.05Na0.95NbO3 shows the coexistence of rhombohedral and monoclinic phases, which indicates that the phase boundary is close to room temperature; the phase boundary for K0.30Na0.70NbO3 is found to be at approximately 180 K

"Asymmetric Market Shares, Advertising, and Pricing: Equilibrium with an Information Gatekeeper"

We analyze the impact of market share on advertising and pricing decisions by firms that sell to loyal, non-shopping customers and can advertise to shoppers through an information intermediary or "gatekeeper." In equilibrium the firm with the smaller loyal market advertises more aggressively but prices less competitively than the firm with the larger loyal market, and there is no equilibrium in which both firms advertise with probability 1. The results differ significantly from earlier literature which assumes all prices are revealed to shoppers and finds that the firm with the smaller loyal market adopts a more competitive pricing strategy. The predictions of the model are consistent with advertising and pricing behavior observed on price comparison websites such as Shopper.com.online markets, E-commerce, market share, information gatekeeper, equilibrium price dispersion, advertising

Chondrocalcinosis is common in the absence of knee involvement

Introduction: We aimed to describe the distribution of radiographic chondrocalcinosis (CC) and to examine whether metacarpophalangeal joint (MCPJ) calcification and CC at other joints occurs in the absence of knee involvement. Methods: This was a cross-sectional study embedded in the Genetics of Osteoarthritis and Lifestyle study (GOAL). All participants (n = 3,170) had radiographs of the knees, hands, and pelvis. These were scored for radiographic changes of osteoarthritis (OA), for CC at knees, hips, symphysis pubis, and wrists, and for MCPJ calcification. The prevalence of MCPJ calcification and CC overall, at each joint, and in the presence or absence of knee involvement, was calculated. Results: The knee was the commonest site of CC, followed by wrists, hips, and symphysis pubis. CC was more likely to be bilateral at knees and wrists but unilateral at hips. MCPJ calcification was usually bilateral, and less common than CC at knees, hips, wrists, and symphysis pubis. Unlike that previously reported, CC commonly occurred without any knee involvement; 44.4% of wrist CC, 45.9% of hip CC, 45.5% of symphysis pubis CC, and 31.3% of MCPJ calcification occurred in patients without knee CC. Those with meniscal or hyaline articular cartilage CC had comparable ages (P = 0.21), and neither preferentially associated with fibrocartilage CC at distant joints. Conclusions: CC visualized on a plain radiograph commonly occurs at other joints in the absence of radiographic knee CC. Therefore, knee radiographs alone are an insufficient screening test for CC. This has significant implications for clinical practice, for epidemiologic and genetic studies of CC, and for the definition of OA patients with coexistent crystal deposition