Sparse deep neural networks have proven to be efficient for predictive model building in large-scale studies. Although several works have studied theoretical and numerical properties of sparse neural architectures, they have primarily focused on the edge selection. Sparsity through edge selection might be intuitively appealing; however, it does not necessarily reduce the structural complexity of a network. Instead pruning excessive nodes in each layer leads to a structurally sparse network which would have lower computational complexity and memory footprint. We propose a Bayesian sparse solution using spike-and-slab Gaussian priors to allow for node selection during training. The use of spike-and-slab prior alleviates the need of an ad-hoc thresholding rule for pruning redundant nodes from a network. In addition, we adopt a variational Bayes approach to circumvent the computational challenges of traditional Markov Chain Monte Carlo (MCMC) implementation. In the context of node selection, we establish the fundamental result of variational posterior consistency together with the characterization of prior parameters. In contrast to the previous works, our theoretical development relaxes the assumptions of the equal number of nodes and uniform bounds on all network weights, thereby accommodating sparse networks with layer-dependent node structures or coefficient bounds. With a layer-wise characterization of prior inclusion probabilities, we also discuss optimal contraction rates of the variational posterior. Finally, we provide empirical evidence to substantiate that our theoretical work facilitates layer-wise optimal node recovery together with competitive predictive performance.
Surgical procedures are commonly performed using mice but can have major effects on their core body temperature, including development of hypothermia. In this study, we evaluated active perioperative warming with and without surgical draping with adherent plastic wrap to refine practices, improve animal welfare, and optimize research experiments. Mice were randomized into treatment groups (n = 6; 8 CD1 mice per group). Treatments included placement within a small-animal forced-air incubator at 38 °C for 30 min before surgery (Pre), after surgery (Post), or before and after surgery (Both). To explore the effect of surgical draping, one group received incubator warming before and after surgery in addition to surgical draping (Both/Drape), whereas another group received surgical draping only without incubator warming (Control/Drape). The final group of mice received neither warming nor draping (Control). Subcutaneous temperature transponders were placed in all mice. Approximately 5 d after transponder placement, mice were anesthetized with ketamine–xylazine and underwent laparotomy. Subcutaneous body temperatures were collected perioperatively from transponders, and rectal temperatures were taken every minute during surgery. For recovery from anesthesia, mice were placed either in a standard cage on a warm water blanket set to 38 °C (100.4 °F) or in the incubator. Subcutaneous body temperatures were significantly higher in mice prewarmed for 30 min (Pre, Both, Both/Drape) as compared with mice that were not prewarmed. Anesthetic recovery times were significantly longer for mice placed in the incubator (Pre, Post, Both, Both/Drape) than for those that did not receive incubator warming (Control, Control/Drape). Mean intraoperative rectal temperatures of Both/Drape mice tended to be greater than those of mice in the Both group, suggesting a warming benefit of surgical draping. Using a forced air incubator and adherent plastic draping mitigated body temperature loss in mice during both surgery and postoperative recovery.
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