Conditionally conjugate mean-field variational Bayes for logistic models

Variational Bayes (VB) is a common strategy for approximate Bayesian inference, but simple methods are only available for specific classes of models including, in particular, representations having conditionally conjugate constructions within an exponential family. Models with logit components are an apparently notable exception to this class, due to the absence of conjugacy between the logistic likelihood and the Gaussian priors for the coefficients in the linear predictor. To facilitate approximate inference within this widely used class of models, Jaakkola and Jordan (2000) proposed a simple variational approach which relies on a family of tangent quadratic lower bounds of logistic log-likelihoods, thus restoring conjugacy between these approximate bounds and the Gaussian priors. This strategy is still implemented successfully, but less attempts have been made to formally understand the reasons underlying its excellent performance. To cover this key gap, we provide a formal connection between the above bound and a recent P\'olya-gamma data augmentation for logistic regression. Such a result places the computational methods associated with the aforementioned bounds within the framework of variational inference for conditionally conjugate exponential family models, thereby allowing recent advances for this class to be inherited also by the methods relying on Jaakkola and Jordan (2000)

A nested expectation-maximization algorithm for latent class models with covariates

We develop a nested EM routine for latent class models with covariates which allows maximization of the full-model log-likelihood and, differently from current methods, guarantees monotone log-likelihood sequences along with improved convergence rates

Evaluating the specific heat loss in severely notched stainless steel specimens for fatigue strength analyses

Abstract In the last years, a large amount of fatigue test results from plain and bluntly notched specimens made of AISI 304L stainless steel were synthetized in a single scatter band adopting the specific heat loss per cycle (Q) as a damage parameter. During a fatigue test, the Q parameter can be evaluated measuring the cooling gradient at a point of the specimens after having suddenly stopped the fatigue test. This measurement can be done by using thermocouples in the case of plain or notched material; however, due to the high stress concentration at the tip of severely notched components analysed in the present paper, an infrared camera achieving a much improved spatial resolution was adopted. A data processing technique is presented to investigate the heat energy distribution close to the notch tip of hot-rolled AISI 304L stainless steel specimens, having notch tip radii equal to 3, 1 and 0.5 mm and subjected to constant amplitude cyclic loads

Bayesian testing for exogenous partition structures in stochastic block models

Network data often exhibit block structures characterized by clusters of nodes with similar patterns of edge formation. When such relational data are complemented by additional information on exogenous node partitions, these sources of knowledge are typically included in the model to supervise the cluster assignment mechanism or to improve inference on edge probabilities. Although these solutions are routinely implemented, there is a lack of formal approaches to test if a given external node partition is in line with the endogenous clustering structure encoding stochastic equivalence patterns among the nodes in the network. To fill this gap, we develop a formal Bayesian testing procedure which relies on the calculation of the Bayes factor between a stochastic block model with known grouping structure defined by the exogenous node partition and an infinite relational model that allows the endogenous clustering configurations to be unknown, random and fully revealed by the block-connectivity patterns in the network. A simple Markov chain Monte Carlo method for computing the Bayes factor and quantifying uncertainty in the endogenous groups is proposed. This strategy is evaluated in simulations, and in applications studying brain networks of Alzheimer's patients

Crack paths in multiaxial fatigue of C45 steel specimens and correlation of lifetime with the thermal energy dissipation

The work reports the observed fatigue damage of C45 steel specimens tested in a previous work under multiaxial loading conditions and its relationship with the thermal energy dissipation which has been used in the last decades to estimate the uniaxial fatigue behavior of metals. For this purpose, fatigue data relevant to thin-walled samples made of quenched and tempered C45 steel tested under completely reversed combined axial and torsional cyclic loadings with different biaxiality ratios and phase-shift angles have been analysed. The analyses of crack paths at the initiation point of failure were performed after a 50% stiffness loss that corresponded to a crack size ranging from 7 to 15 mm; afterwards, the characteristic crack paths of each loading condition were analysed by using a digital microscope to identify the orientation of the crack initiation plane. After having broken all fatigue tested specimens under static tensile loading, the fracture surfaces were inspected close to the crack initiation point using a digital microscope. Despite the stress states and fatigue damage mechanisms dependent on the load condition, the Q parameter applied to the present experimental results proved to correlate all multiaxial fatigue test results in a single fatigue scatter band

Extended Stochastic Block Models with Application to Criminal Networks

Reliably learning group structure among nodes in network data is challenging in modern applications. We are motivated by covert networks encoding relationships among criminals. These data are subject to measurement errors and exhibit a complex combination of an unknown number of core-periphery, assortative and disassortative structures that may unveil the internal architecture of the criminal organization. The coexistence of such noisy block structures limits the reliability of community detection algorithms routinely applied to criminal networks, and requires extensions of model-based solutions to realistically characterize the node partition process, incorporate information from node attributes, and provide improved strategies for estimation, uncertainty quantification, model selection and prediction. To address these goals, we develop a novel class of extended stochastic block models (ESBM) that infer groups of nodes having common connectivity patterns via Gibbs-type priors on the partition process. This choice encompasses several realistic priors for criminal networks, covering solutions with fixed, random and infinite number of possible groups, and facilitates inclusion of node attributes in a principled manner. Among the new alternatives in our class, we focus on the Gnedin process as a realistic prior that allows the number of groups to be finite, random and subject to a reinforcement process coherent with the modular structures in organized crime. A collapsed Gibbs sampler is proposed for the whole ESBM class, and refined strategies for estimation, prediction, uncertainty quantification and model selection are outlined. ESBM performance is illustrated in realistic simulations and in an application to an Italian Mafia network, where we learn key block patterns revealing a complex hierarchical structure of the organization, mostly hidden from state-of-the-art alternative solutions

Analysis of dissipated energy and temperature fields at severe notches of AISI 304L stainless steel specimens

In the last years, a large amount of fatigue test results from plain and bluntly notched specimens made of AISI 304L stainless steel were synthetized in a single scatter band by adopting the specific heat loss per cycle (Q) as a damage parameter. During a fatigue test, the Q parameter can be evaluated measuring the cooling gradient at a point of the specimens after having suddenly stopped the fatigue test. This measurement can be done by using thermocouples; however, due to the high stress concentration at the tip of severely notched components analysed in the present paper, an infrared camera achieving a much improved spatial resolution was adopted. A data processing technique is presented to investigate the heat energy distribution close to the notch tip of hot-rolled AISI 304L stainless steel specimens, having notch tip radii equal to 3, 1 and 0.5 mm and subjected to constant amplitude cyclic loads. A thermal finite element analysis was also performed by assigning heat generation in the appropriate region close to the notch tip. Then the numerical temperature values were compared with the experimental measurement

analysis of dissipated energy and temperature fields at severe notches of aisi 304l stainless steel specimens

In the last years, a large amount of fatigue test results from plain and bluntly notched specimens made of AISI 304L stainless steel were synthetized in a single scatter band by adopting the specific heat loss per cycle (Q) as a damage parameter. During a fatigue test, the Q parameter can be evaluated measuring the cooling gradient at a point of the specimens after having suddenly stopped the fatigue test. This measurement can be done by using thermocouples; however, due to the high stress concentration at the tip of severely notched components analysed in the present paper, an infrared camera achieving a much improved spatial resolution was adopted. A data processing technique is presented to investigate the heat energy distribution close to the notch tip of hot-rolled AISI 304L stainless steel specimens, having notch tip radii equal to 3, 1 and 0.5 mm and subjected to constant amplitude cyclic loads. A thermal finite element analysis was also performed by assigning heat generation in the appropriate region close to the notch tip. Then the numerical temperature values were compared with the experimental measurement