Mixtures of Common Skew-t Factor Analyzers

A mixture of common skew-t factor analyzers model is introduced for model-based clustering of high-dimensional data. By assuming common component factor loadings, this model allows clustering to be performed in the presence of a large number of mixture components or when the number of dimensions is too large to be well-modelled by the mixtures of factor analyzers model or a variant thereof. Furthermore, assuming that the component densities follow a skew-t distribution allows robust clustering of skewed data. The alternating expectation-conditional maximization algorithm is employed for parameter estimation. We demonstrate excellent clustering performance when our model is applied to real and simulated data.This paper marks the first time that skewed common factors have been used

Mixtures of Skew-t Factor Analyzers

In this paper, we introduce a mixture of skew-t factor analyzers as well as a family of mixture models based thereon. The mixture of skew-t distributions model that we use arises as a limiting case of the mixture of generalized hyperbolic distributions. Like their Gaussian and t-distribution analogues, our mixture of skew-t factor analyzers are very well-suited to the model-based clustering of high-dimensional data. Imposing constraints on components of the decomposed covariance parameter results in the development of eight flexible models. The alternating expectation-conditional maximization algorithm is used for model parameter estimation and the Bayesian information criterion is used for model selection. The models are applied to both real and simulated data, giving superior clustering results compared to a well-established family of Gaussian mixture models

Obscuration by Gas and Dust in Luminous Quasars

We explore the connection between absorption by neutral gas and extinction by dust in mid-infrared (IR) selected luminous quasars. We use a sample of 33 quasars at redshifts 0.7 < z < 3 in the 9 deg^2 Bo\"otes multiwavelength survey field that are selected using Spitzer Space Telescope Infrared Array Camera colors and are well-detected as luminous X-ray sources (with >150 counts) in Chandra observations. We divide the quasars into dust-obscured and unobscured samples based on their optical to mid-IR color, and measure the neutral hydrogen column density N_H through fitting of the X-ray spectra. We find that all subsets of quasars have consistent power law photon indices equal to 1.9 that are uncorrelated with N_H. We classify the quasars as gas-absorbed or gas-unabsorbed if N_H > 10^22 cm^-2 or N_H < 10^22 cm^-2, respectively. Of 24 dust-unobscured quasars in the sample, only one shows clear evidence for significant intrinsic N_H, while 22 have column densities consistent with N_H < 10^22 cm^-2. In contrast, of the nine dust-obscured quasars, six show evidence for intrinsic gas absorption, and three are consistent with N_H < 10^22 cm^-2. We conclude that dust extinction in IR-selected quasars is strongly correlated with significant gas absorption as determined through X-ray spectral fitting. These results suggest that obscuring gas and dust in quasars are generally co-spatial, and confirm the reliability of simple mid-IR and optical photometric techniques for separating quasars based on obscuration.Comment: 5 pages, 3 figure

Parsimonious Shifted Asymmetric Laplace Mixtures

A family of parsimonious shifted asymmetric Laplace mixture models is introduced. We extend the mixture of factor analyzers model to the shifted asymmetric Laplace distribution. Imposing constraints on the constitute parts of the resulting decomposed component scale matrices leads to a family of parsimonious models. An explicit two-stage parameter estimation procedure is described, and the Bayesian information criterion and the integrated completed likelihood are compared for model selection. This novel family of models is applied to real data, where it is compared to its Gaussian analogue within clustering and classification paradigms

Disentangling within-person changes and individual differences among fundamental need satisfaction, attainment of acquisitive desires, and psychological health

We explored within-person and individual difference associations among basic psychological need satisfaction (autonomy, competence, and relatedness), attainment of acquisitive desires (wealth and popularity) and indicators of well- and ill-being. Participants were 198 undergraduates (51% male) who completed an inventory multiple times over a university semester. Analyses revealed that increased satisfaction of all the needs and desires beyond participants’ normal levels, with the exception of relatedness, were associated with greater psychological welfare. Nonetheless, individual differences in well-being were only predicted by psychological need satisfaction, and not by the attainment of acquisitive desires. Hence, the realization of acquisitive desires may elicit within-person increases in psychological welfare; however, satisfying innate needs may be a better bet for long term psychological health

Relations and Equivalences Between Circuit Lower Bounds and Karp-Lipton Theorems

A frontier open problem in circuit complexity is to prove P^{NP} is not in SIZE[n^k] for all k; this is a necessary intermediate step towards NP is not in P_{/poly}. Previously, for several classes containing P^{NP}, including NP^{NP}, ZPP^{NP}, and S_2 P, such lower bounds have been proved via Karp-Lipton-style Theorems: to prove C is not in SIZE[n^k] for all k, we show that C subset P_{/poly} implies a "collapse" D = C for some larger class D, where we already know D is not in SIZE[n^k] for all k. It seems obvious that one could take a different approach to prove circuit lower bounds for P^{NP} that does not require proving any Karp-Lipton-style theorems along the way. We show this intuition is wrong: (weak) Karp-Lipton-style theorems for P^{NP} are equivalent to fixed-polynomial size circuit lower bounds for P^{NP}. That is, P^{NP} is not in SIZE[n^k] for all k if and only if (NP subset P_{/poly} implies PH subset i.o.- P^{NP}_{/n}). Next, we present new consequences of the assumption NP subset P_{/poly}, towards proving similar results for NP circuit lower bounds. We show that under the assumption, fixed-polynomial circuit lower bounds for NP, nondeterministic polynomial-time derandomizations, and various fixed-polynomial time simulations of NP are all equivalent. Applying this equivalence, we show that circuit lower bounds for NP imply better Karp-Lipton collapses. That is, if NP is not in SIZE[n^k] for all k, then for all C in {Parity-P, PP, PSPACE, EXP}, C subset P_{/poly} implies C subset i.o.-NP_{/n^epsilon} for all epsilon > 0. Note that unconditionally, the collapses are only to MA and not NP. We also explore consequences of circuit lower bounds for a sparse language in NP. Among other results, we show if a polynomially-sparse NP language does not have n^{1+epsilon}-size circuits, then MA subset i.o.-NP_{/O(log n)}, MA subset i.o.-P^{NP[O(log n)]}, and NEXP is not in SIZE[2^{o(m)}]. Finally, we observe connections between these results and the "hardness magnification" phenomena described in recent works