Stability selection is a widely adopted resampling-based framework for high-dimensional structure estimation and variable selection. However, the concept of 'stability' is often narrowly addressed, primarily through examining selection frequencies, or 'stability paths'. This paper seeks to broaden the use of an established stability estimator to evaluate the overall stability of the stability selection framework, moving beyond single-variable analysis. We suggest that the stability estimator offers two advantages: it can serve as a reference to reflect the robustness of the outcomes obtained and help identify an optimal regularization value to improve stability. By determining this value, we aim to calibrate key stability selection parameters, namely, the decision threshold and the expected number of falsely selected variables, within established theoretical bounds. Furthermore, we explore a novel selection criterion based on this regularization value. With the asymptotic distribution of the stability estimator previously established, convergence to true stability is ensured, allowing us to observe stability trends over successive sub-samples. This approach sheds light on the required number of sub-samples addressing a notable gap in prior studies. The 'stabplot' package is developed to facilitate the use of the plots featured in this manuscript, supporting their integration into further statistical analysis and research workflows.

Paper Summary: The main idea is that Nesterov's acceleration method's and Stochastic Gradient Descent's (SGD) advantages are used to solve sparse and dense optimization problems with high-dimensions by using an improved GCD (Greedy Coordinate Descent) algorithm. First, by using a greedy rule, an l_1 -square-regularized approximate optimization problem (find a solution close to x * within a neighborhood \epsilon) can be reformulated as a convex but non-trivial to solve problem. Then, the same problem is solved as an exact problem by using the SOTOPO algorithm. Finally, the solution is improved by using both the convergence rate advantage of Nesterov's method and the "reduced-by-one-sample" complexity of SGD. The resulted algorithm is an improved GCD (ASGCD Accelerated Stochastic Greedy Coordinate Descent) with a convergence rate of O(\sqrt{1/\epsilon}) and complexity reduced-by-one-sample compared to the vanilla GCD.

Data, especially private data, has become increasingly valuable in the modern era. From hospital records to personal search histories, the increased collection and use of private data means that data analysis conducted on these data sets must protect sensitive information about individuals. Without this protection, a leak of sensitive information could easily have lasting consequences for an individual, even from seemingly innocuous data like a photo. The rise of machine learning has exacerbated these concerns even further due to its need for specific and abundant data to produce accurate predictions. This large amount of required data and machine learning models' tendency to memorize specific yet unnecessary information, such as specific IP addresses during text responses, makes private machine learning especially important[1].

We investigate filter level sparsity that emerges in convolutional neural networks (CNNs) which employ Batch Normalization and ReLU activation, and are trained with adaptive gradient descent techniques and L2 regularization (or weight decay). We conduct an extensive experimental study casting these initial findings into hypotheses and conclusions about the mechanisms underlying the emergent filter level sparsity. This study allows new insight into the performance gap obeserved between adapative and non-adaptive gradient descent methods in practice. Further, analysis of the effect of training strategies and hyperparameters on the sparsity leads to practical suggestions in designing CNN training strategies enabling us to explore the tradeoffs between feature selectivity, network capacity, and generalization performance. Lastly, we show that the implicit sparsity can be harnessed for neural network speedup at par or better than explicit sparsification / pruning approaches, without needing any modifications to the typical training pipeline.

There are 2 aspects of this research that are worth highlighting: (1) we showed that micro-structural extra-hippocampal abnormalities are consistent enough across medial temporal lobe epilepsy (TLE) patients that they can be used to predict TLE, and (2) we obtained regularization values for the models trained on this sparse data in an unusual but effective manner. Our input data consisted of 3 different diffusion imaging modalities: mean diffusivity (MD), fractional anisotropy (FA), and mean kurtosis (MK). Predictive models trained with MK proved to be the most accurate: .82 Also, the highest coefficients of these linear models were located within the inferior medial aspect of the temporal lobes. These locations have complex fiber anatomy with many crossings. Diffusion kurtosis imaging (DKI) is more apt than diffusion tensor imaging (DTI) at capturing fiber crossings due to the presence of non-Gaussian water diffusion.