Bias-Variance Trade-Off in Hierarchical Probabilistic Models Using Higher-Order Feature Interactions

Hierarchical probabilistic models are able to use a large number of parameters to create a model with a high representation power. However, it is well known that increasing the number of parameters also increases the complexity of the model which leads to a bias-variance trade-off. Although it is a classical problem, the bias-variance trade-off between hidden layers and higher-order interactions have not been well studied. In our study, we propose an efficient inference algorithm for the log-linear formulation of the higher-order Boltzmann machine using a combination of Gibbs sampling and annealed importance sampling. We then perform a bias-variance decomposition to study the differences in hidden layers and higher-order interactions. Our results have shown that using hidden layers and higher-order interactions have a comparable error with a similar order of magnitude and using higher-order interactions produce less variance for smaller sample size.Comment: 8 pages, 28 figures, accepted to the Thirty-Third AAAI Conference on Artificial Intelligence (AAAI-19

Bioactive SrO-SiO2 glass with well-ordered mesopores: Characterization, physiochemistry and biological properties

For a biomaterial to be considered suitable for bone repair it should ideally be both bioactive and have a capacity for controllable drug delivery; as such, mesoporous SiO2 glass has been proposed as a new class of bone regeneration material by virtue of its high drug-loading ability and generally good biocompatibility. It does, however, have less than optimum bioactivity and controllable drug delivery properties. In this study, we incorporated strontium (Sr) into mesoporous SiO2 in an effort to develop a bioactive mesoporous SrO–SiO2 (Sr–Si) glass with the capacity to deliver Sr2+ ions, as well as a drug, at a controlled rate, thereby producing a material better suited for bone repair. The effects of Sr2+ on the structure, physiochemistry, drug delivery and biological properties of mesoporous Sr–Si glass were investigated. The prepared mesoporous Sr–Si glass was found to have an excellent release profile of bioactive Sr2+ ions and dexamethasone, and the incorporation of Sr2+ improved structural properties, such as mesopore size, pore volume and specific surface area, as well as rate of dissolution and protein adsorption. The mesoporous Sr–Si glass had no cytotoxic effects and its release of Sr2+ and SiO44− ions enhanced alkaline phosphatase activity – a marker of osteogenic cell differentiation – in human bone mesenchymal stem cells. Mesoporous Sr–Si glasses can be prepared to porous scaffolds which show a more sustained drug release. This study suggests that incorporating Sr2+ into mesoporous SiO2 glass produces a material with a more optimal drug delivery profile coupled with improved bioactivity, making it an excellent material for bone repair applications. Keywords: Mesoporous Sr–Si glass; Drug delivery; Bioactivity; Bone repair; Scaffold

Concurrent encoding of frequency and amplitude modulation in human auditory cortex: MEG evidence

September 26, 2007; doi:10.1152/jn.00342.2007. Complex natural sounds (e.g., animal vocalizations or speech) can be characterized by specific spectrotemporal patterns the components of which change in both frequency (FM) and amplitude (AM). The neural coding of AM and FM has been widely studied in humans and animals but typically with either pure AM or pure FM stimuli. The neural mechanisms employed to perceptually unify AM and FM acoustic features remain unclear. Using stimuli with simultaneous sinusoidal AM (at rate f AM � 37 Hz) and FM (with varying rates ƒ FM), magnetoencephalography (MEG) is used to investigate the elicited auditory steady-state response (aSSR) at relevant frequencies (ƒ AM, ƒ FM, ƒ AM � f FM). Previous work demonstrated that for sounds with slower FM dynamics (f FM � 5 Hz), the phase of the aSSR at ƒ AM tracked the FM; in other words, AM and FM features were co-tracked and co-represented by “phase modulation ” encoding. This stud