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In this paper, we propose a new framework to construct confidence sets for a $d$-dimensional unknown sparse parameter ${\boldsymbol \theta }$ under the normal mean model ${\boldsymbol X}\sim N({\boldsymbol \theta },\sigma ^{2}\bf{I})$. A key feature of the proposed confidence set is its capability to account for the sparsity of ${\boldsymbol \theta }$, thus named as sparse confidence set. This is in sharp contrast with the classical methods, such as the Bonferroni confidence intervals and other resampling-based procedures, where the sparsity of ${\boldsymbol \theta }$ is often ignored. Specifically, we require the desired sparse confidence set to satisfy the following two conditions: (i) uniformly over the parameter space, the coverage probability for ${\boldsymbol \theta }$ is above a pre-specified level; (ii) there exists a random subset $S$ of $\{1,...,d\}$ such that $S$ guarantees the pre-specified true negative rate for detecting non-zero $\theta _{j}$’s. To exploit the sparsity of ${\boldsymbol \theta }$, we allow the confidence interval for $\theta _{j}$ to degenerate to a single point 0 for any $j\notin S$. Under this new framework, we first consider whether there exist sparse confidence sets that satisfy the above two conditions. To address this question, we establish a non-asymptotic minimax lower bound for the non-coverage probability over a suitable class of sparse confidence sets. The lower bound deciphers the role of sparsity and minimum signal-to-noise ratio (SNR) in the construction of sparse confidence sets. Furthermore, under suitable conditions on the SNR, a two-stage procedure is proposed to construct a sparse confidence set. To evaluate the optimality, the proposed sparse confidence set is shown to attain a minimax lower bound of some properly defined risk function up to a constant factor. Finally, we develop an adaptive procedure to the unknown sparsity. Numerical studies are conducted to verify the theoretical results.

 

With the explosive growth of biomarker data in Alzheimer’s disease (AD) clinical trials, numerous mathematical models have been developed to characterize disease-relevant biomarker trajectories over time. While some of these models are purely empiric, others are causal, built upon various hypotheses of AD pathophysiology, a complex and incompletely understood area of research. One of the most challenging problems in computational causal modeling is using a purely data-driven approach to derive the model’s parameters and the mathematical model itself, without any prior hypothesis bias. In this paper, we develop an innovative data-driven modeling approach to build and parameterize a causal model to characterize the trajectories of AD biomarkers. This approach integrates causal model learning, population parameterization, parameter sensitivity analysis, and personalized prediction. By applying this integrated approach to a large multicenter database of AD biomarkers, the Alzheimer’s Disease Neuroimaging Initiative, several causal models for different AD stages are revealed. In addition, personalized models for each subject are calibrated and provide accurate predictions of future cognitive status.

 

The quantification of microstructural properties to optimize battery design and performance, to maintain product quality, or to track the degradation of LIBs remains expensive and slow when performed through currently used characterization approaches. In this paper, a convolution neural network-based deep learning approach (CNN) is reported to infer electrode microstructural properties from the inexpensive, easy to measure cell voltage versus capacity data. The developed framework combines two CNN models to balance the bias and variance of the overall predictions. As an example application, the method was demonstrated against porous electrode theory-generated voltage versus capacity plots. For the graphite|LiMn$$_2$$${}_2$O$$_4$$${}_4$chemistry, each voltage curve was parameterized as a function of the cathode microstructure tortuosity and area density, delivering CNN predictions of Bruggeman’s exponent and shape factor with 0.97$$R^2$$$R^2$score within 2 s each, enabling to distinguish between different types of particle morphologies, anisotropies, and particle alignments. The developed neural network model can readily accelerate the processing-properties-performance and degradation characteristics of the existing and emerging LIB chemistries.

 

In this paper, we study the problem of inference in high-order structured prediction tasks. In the context of Markov random fields, the goal of a high-order inference task is to maximize a score function on the space of labels, and the score function can be decomposed into sum of unary and high-order potentials. We apply a generative model approach to study the problem of high-order inference, and provide a two-stage convex optimization algorithm for exact label recovery. We also provide a new class of hypergraph structural properties related to hyperedge expansion that drives the success in general high-order inference problems. Finally, we connect the performance of our algorithm and the hyperedge expansion property using a novel hypergraph Cheeger-type inequality. 

We develop a novel method to remove injected backdoors in deep learning models. It works by cloning the benign behaviors of a trojaned model to a new model of the same structure. It trains the clone model from scratch on a very small subset of samples and aims to minimize a cloning loss that denotes the differences between the activations of important neurons across the two models. The set of important neurons varies for each input, depending on their magnitude of activations and their impact on the classification result. We theoretically show our method can better recover benign functions of the backdoor model. Meanwhile, we prove our method can be more effective in removing backdoors compared with fine-tuning. Our experiments show that our technique can effectively remove nine different types of backdoors with minor benign accuracy degradation, outperforming the state-of-the-art backdoor removal techniques that are based on fine-tuning, knowledge distillation, and neuron pruning. 

Parallel tempering (PT), also known as replica exchange, is the go-to workhorse for simulations of multi-modal distributions. The key to the success of PT is to adopt efficient swap schemes. The popular deterministic even-odd (DEO) scheme exploits the non-reversibility property and has successfully reduced the communication cost from O(P 2) to O(P) given sufficient many P chains. However, such an innovation largely disappears in big data problems due to the limited chains and extremely few bias-corrected swaps. To handle this issue, we generalize the DEO scheme to promote the non-reversibility and obtain an appealing communication cost O(P log P) based on the optimal window size. In addition, we also analyze the bias when we adopt stochastic gradient descent (SGD) with large and constant learning rates as exploration kernels. Such a user-friendly nature enables us to conduct large-scale uncertainty approximation tasks without much tuning costs.