Global Sensitivity Analysis for MAP Inference in Graphical Models

We study the sensitivity of a MAP configuration of a discrete probabilistic graphical model with respect to perturbations of its parameters. These perturbations are global, in the sense that simultaneous perturbations of all the parameters (or any chosen subset of them) are allowed. Our main contribution is an exact algorithm that can check whether the MAP configuration is robust with respect to given perturbations. Its complexity is essentially the same as that of obtaining the MAP configuration itself, so it can be promptly used with minimal effort. We use our algorithm to identify the largest global perturbation that does not induce a change in the MAP configuration, and we successfully apply this robustness measure in two practical scenarios: the prediction of facial action units with posed images and the classification of multiple real public data sets. A strong correlation between the proposed robustness measure and accuracy is verified in both scenarios.

Probabilistic Inference in Credal Networks: New Complexity Results

Credal networks are graph-based statistical models whose parameters take values in a set, instead of being sharply specified as in traditional statistical models (e.g., Bayesian networks). The computational complexity of inferences on such models depends on the irrelevance/independence concept adopted. In this paper, we study inferential complexity under the concepts of epistemic irrelevance and strong independence. We show that inferences under strong independence are NP-hard even in trees with binary variables except for a single ternary one. We prove that under epistemic irrelevance the polynomial-time complexity of inferences in credal trees is not likely to extend to more general models (e.g., singly connected topologies). These results clearly distinguish networks that admit efficient inferences and those where inferences are most likely hard, and settle several open questions regarding their computational complexity. We show that these results remain valid even if we disallow the use of zero probabilities. We also show that the computation of bounds on the probability of the future state in a hidden Markov model is the same whether we assume epistemic irrelevance or strong independence, and we prove an analogous result for inference in Naive Bayes structures. These inferential equivalences are important for practitioners, as hidden Markov models and Naive Bayes networks are used in real applications of imprecise probability.

5.9-keV Mn K-shell X-ray luminosity from the decay of 55Fe in Type Ia supernova models

We show that the X-ray line flux of the Mn Kα line at 5.9 keV from the decay of 55Fe is a promising diagnostic to distinguish between Type Ia supernova (SN Ia) explosion models. Using radiation transport calculations, we compute the line flux for two three-dimensional explosion models: a near-Chandrasekhar mass delayed detonation and a violent merger of two (1.1 and 0.9 M⊙) white dwarfs. Both models are based on solar metallicity zero-age main-sequence progenitors. Due to explosive nuclear burning at higher density, the delayed-detonation model synthesizes ˜3.5 times more radioactive 55Fe than the merger model. As a result, we find that the peak Mn Kα line flux of the delayed-detonation model exceeds that of the merger model by a factor of ˜4.5. Since in both models the 5.9-keV X-ray flux peaks five to six years after the explosion, a single measurement of the X-ray line emission at this time can place a constraint on the explosion physics that is complementary to those derived from earlier phase optical spectra or light curves. We perform detector simulations of current and future X-ray telescopes to investigate the possibilities of detecting the X-ray line at 5.9 keV. Of the currently existing telescopes, XMM-Newton/pn is the best instrument for close (≲1-2 Mpc), non-background limited SNe Ia because of its large effective area. Due to its low instrumental background, Chandra/ACIS is currently the best choice for SNe Ia at distances above ˜2 Mpc. For the delayed-detonation scenario, a line detection is feasible with Chandra up to ˜3 Mpc for an exposure time of 106 s. We find that it should be possible with currently existing X-ray instruments (with exposure times ≲5 × 105 s) to detect both of our models at sufficiently high S/N to distinguish between them for hypothetical events within the Local Group. The prospects for detection will be better with future missions. For example, the proposed Athena/X-IFU instrument could detect our delayed-detonation model out to a distance of ˜5 Mpc. This would make it possible to study future events occurring during its operational life at distances comparable to those of the recent supernovae SN 2011fe (˜6.4 Mpc) and SN 2014J (˜3.5 Mpc).

Hidden Markov Models With Set-Valued Parameters

Hidden Markov models (HMMs) are widely used probabilistic models of sequential data. As with other probabilistic models, they require the specification of local conditional probability distributions, whose assessment can be too difficult and error-prone, especially when data are scarce or costly to acquire. The imprecise HMM (iHMM) generalizes HMMs by allowing the quantification to be done by sets of, instead of single, probability distributions. iHMMs have the ability to suspend judgment when there is not enough statistical evidence, and can serve as a sensitivity analysis tool for standard non-stationary HMMs. In this paper, we consider iHMMs under the strong independence interpretation, for which we develop efficient inference algorithms to address standard HMM usage such as the computation of likelihoods and most probable explanations, as well as performing filtering and predictive inference. Experiments with real data show that iHMMs produce more reliable inferences without compromising the computational efficiency.

Choice of commuting mode among employees: Do home neighborhood environment, worksite neighborhood environment, and worksite policy and supports matter?

BACKGROUND: Promoting the use of public transit and active transport (walking and cycling) instead of car driving is an appealing strategy to increase overall physical activity.

PURPOSE: To quantify the combined associations between self-reported home and worksite neighborhood environments, worksite support and policies, and employees' commuting modes.

METHOD: Between 2012 and 2013, participants residing in four Missouri metropolitan areas were interviewed via telephone (n = 1,338) and provided information on socio-demographic characteristics, home and worksite neighborhoods, and worksite support and policies. Commuting mode was self-reported and categorized into car driving, public transit, and active commuting. Commuting distance was calculated using geographic information systems. Commuters providing completed data were included in the analysis. Multivariate logistic regression models were used to examine the correlates of using public transit and active commuting.

RESULT: The majority of participants reported commuting by driving (88.9%); only 4.9% used public transit and 6.2% used active modes. After multivariate adjustment, having transit stops within 10-15 minutes walking distance from home (p=0.05) and using worksite incentive for public transit (p<0.001) were associated with commuting by public transit. Commuting distance (p<0.001) was negatively associated with active commuting. Having free or low cost recreation facilities around the worksite (p=0.04) and using bike facilities to lock bikes at the worksite (p<0.001) were associated with active commuting.

CONCLUSION: Both environment features and worksite supports and policies are associated with the choice of commuting mode. Future studies should use longitudinal designs to investigate the potential of promoting alternative commuting modes through worksite efforts that support sustainable commuting behaviors as well as the potential of built environment improvements.

Partial Cooperation in Location Choice: Salop’s Model with Three Firms

We consider how three firms compete in a Salop location model and how cooperation in location choice by two of these firms affects the outcomes. We con- sider the classical case of linear transportation costs as a two-stage game in which the firms select first a location on a unit circle along which consumers are dispersed evenly, followed by the competitive selection of a price. Standard analysis restricts itself to purely competitive selection of location; instead, we focus on the situation in which two firms collectively decide about location, but price their products competitively after the location choice has been effectuated. We show that such partial coordination of location is beneficial to all firms, since it reduces the number of equilibria significantly and, thereby, the resulting coordination problem. Subsequently, we show that the case of quadratic transportation costs changes the main conclusions only marginally.