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We propose a new approach, the calibrated nonparametric scan statistic (CNSS), for more accurate detection of anomalous patterns in large-scale, real-world graphs. Scan statistics identify connected subgraphs that are interesting or…
Finding the sparse representation of a signal in an overcomplete dictionary has attracted a lot of attention over the past years. This paper studies ProSparse, a new polynomial complexity algorithm that solves the sparse representation…
Estimation of structure, such as in variable selection, graphical modelling or cluster analysis is notoriously difficult, especially for high-dimensional data. We introduce stability selection. It is based on subsampling in combination with…
The rapid influx of data-driven models into the industrial sector has been facilitated by the proliferation of sensor technology, enabling the collection of vast quantities of data. However, leveraging these models for failure detection and…
Using well-known mathematical problems for encryption is a widely used technique because they are computationally hard and provide security against potential attacks on the encryption method. The subset sum problem (SSP) can be defined as…
The recently proposed stochastic Polyak stepsize (SPS) and stochastic line-search (SLS) for SGD have shown remarkable effectiveness when training over-parameterized models. However, in non-interpolation settings, both algorithms only…
An algorithm is proposed for solving stochastic and finite sum minimization problems. Based on a trust region methodology, the algorithm employs normalized steps, at least as long as the norms of the stochastic gradient estimates are within…
The hidden subgroup problem ($\mathsf{HSP}$) has been attracting much attention in quantum computing, since several well-known quantum algorithms including Shor algorithm can be described in a uniform framework as quantum methods to address…
The stochastic Polyak step size (SPS) has proven to be a promising choice for stochastic gradient descent (SGD), delivering competitive performance relative to state-of-the-art methods on smooth convex and non-convex optimization problems,…
We propose a Similarity-Based Stratified Splitting (SBSS) technique, which uses both the output and input space information to split the data. The splits are generated using similarity functions among samples to place similar samples in…
Compressed sensing (CS) is a valuable technique for reconstructing measurements in numerous domains. CS has not yet gained widespread adoption in scanning tunneling microscopy (STM), despite potentially offering the advantages of lower…
As large language models are increasingly utilized in real-world applications, guarantees of task-specific metrics are essential for their reliable deployment. Previous studies have introduced various criteria of conformal uncertainty…
The Unbounded Subset-Sum Problem (USSP) is defined as: given sum $s$ and a set of integers $W\leftarrow \{p_1,\dots,p_n\}$ output a set of non-negative integers $\{y_1,\dots,y_n\}$ such that $p_1y_1+\dots+p_ny_n=s$. The USSP is an…
Sample reuse techniques have significantly reduced the numerical complexity of probabilistic robustness analysis. Existing results show that for a nested collection of hyper-spheres the complexity of the problem of performing $N$ equivalent…
This is a technical report that extends and clarifies the results presented in [1]. The model identification problem for asymptotically stable linear time invariant systems is considered. The system output is affected by an additive noise…
Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…
Semidefinite programs (SDPs) are standard convex problems that are frequently found in control and optimization applications. Interior-point methods can solve SDPs in polynomial time up to arbitrary accuracy, but scale poorly as the size of…
The problem of model identification for linear systems is considered, using a finite set of sampled data affected by a bounded measurement noise, with unknown bound. The objective is to identify one-step-ahead models and their accuracy in…
Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…
Towards a solution to the sign problem in the simulations of systems having indefinite or complex-valued measures, we propose a new approach which yields statistical errors smaller than the crude Monte Carlo using absolute values of the…