Related papers: Towards a data-scale independent regulariser for r…
Speculative decoding and dynamic sparse attention are two complementary approaches for accelerating long-context LLM inference: the former amortizes target-model execution across multiple verifier queries, while the latter reduces each…
The ability to discover physical laws and governing equations from data is one of humankind's greatest intellectual achievements. A quantitative understanding of dynamic constraints and balances in nature has facilitated rapid development…
Low complexity of a system model is essential for its use in real-time applications. However, sparse identification methods commonly have stringent requirements that exclude them from being applied in an industrial setting. In this paper,…
Stochastic dynamics on sparse graphs and disordered systems often lead to complex behaviors characterized by heterogeneity in time and spatial scales, slow relaxation, localization, and aging phenomena. The mathematical tools and…
Microgrids (MGs) play a crucial role in utilizing distributed energy resources (DERs) like solar and wind power, enhancing the sustainability and flexibility of modern power systems. However, the inherent variability in MG topology, power…
We develop methods for parameter estimation in settings with large-scale data sets, where traditional methods are no longer tenable. Our methods rely on stochastic approximations, which are computationally efficient as they maintain one…
Deep clustering (DC) has become the state-of-the-art for unsupervised clustering. In principle, DC represents a variety of unsupervised methods that jointly learn the underlying clusters and the latent representation directly from…
Seismic data often undergoes severe noise due to environmental factors, which seriously affects subsequent applications. Traditional hand-crafted denoisers such as filters and regularizations utilize interpretable domain knowledge to design…
This thesis focuses on the discovery of stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs) from noisy and discrete time series. A major challenge is selecting the simplest possible correct model…
Compressive sensing (CS) is a data acquisition technique that measures sparse or compressible signals at a sampling rate lower than their Nyquist rate. Results show that sparse signals can be reconstructed using greedy algorithms, often…
High-dimensional learning problems, where the number of features exceeds the sample size, often require sparse regularization for effective prediction and variable selection. While established for fully supervised data, these techniques…
Covariance Neural Networks (VNNs) perform graph convolutions on the covariance matrix of input data to leverage correlation information as pairwise connections. They have achieved success in a multitude of applications such as neuroscience,…
The discovery of governing equations from scientific data has the potential to transform data-rich fields that lack well-characterized quantitative descriptions. Advances in sparse regression are currently enabling the tractable…
We present a weak formulation and discretization of the system discovery problem from noisy measurement data. This method of learning differential equations from data fits into a new class of algorithms that replace pointwise derivative…
The Weak-form Sparse Identification of Nonlinear Dynamics algorithm (WSINDy) has been demonstrated to offer coarse-graining capabilities in the context of interacting particle systems (https://doi.org/10.1016/j.physd.2022.133406). In this…
The singular value decomposition (SVD) is a crucial tool in machine learning and statistical data analysis. However, it is highly susceptible to outliers in the data matrix. Existing robust SVD algorithms often sacrifice speed for…
We introduce a clipping strategy for Stochastic Gradient Descent (SGD) which uses quantiles of the gradient norm as clipping thresholds. We prove that this new strategy provides a robust and efficient optimization algorithm for smooth…
Classical stochastic gradient methods are well suited for minimizing expected-value objective functions. However, they do not apply to the minimization of a nonlinear function involving expected values or a composition of two expected-value…
Certifying neural network robustness against adversarial examples is challenging, as formal guarantees often require solving non-convex problems. Hence, incomplete verifiers are widely used because they scale efficiently and substantially…
Variance reduction (VR) methods employ stochastic gradients with decreasing variance, and they have been widely applied to solve large-scale optimization problems in machine learning because of their efficiency. Existing theoretical studies…