Probabilistic linear solvers (PLSs) return probability distributions that quantify uncertainty due to limited computation in the solution of linear systems. The literature has traditionally distinguished between Bayesian PLSs, which condition a prior on information obtained from projections of the linear system, and probabilistic iterative methods (PIMs), which lift classical iterative solvers to probability space. In this work we show this dichotomy to be false: Bayesian PLSs are a special case of non-stationary affine PIMs. In addition, we prove that any realistic affine PIM is calibrated. These results motivate a focus on (non-stationary) affine PIMs, but their practical adoption has been limited by the significant manual effort required to implement them. To address this, we introduce affine tracing, an algorithmic framework that automatically constructs a PIM from a standard implementation of an affine iterative method by passing symbolic tracers through the computation to build an affine computational graph. We show how this graph can be transformed to compute posterior covariances, and how equality saturation can be used to perform algebraic simplifications required for computation under specific prior choices. We demonstrate the framework by automatically generating a probabilistic multigrid solver and evaluate its performance in the context of Gaussian process approximation.

Here we address the convergence of subspace iteration when distances are measured in the`2 norm andprovide deterministic bounds.

Several problems in machine learning, statistics, and other fields rely on computing eigenvectors. For large scale problems, the computation of these eigenvectors is typically performed via iterative schemes such as subspace iteration or Krylov methods. While there is classical and comprehensive analysis for subspace convergence guarantees with respect to the spectral norm, in many modern applications other notions of subspace distance are more appropriate. Recent theoretical work has focused on perturbations of subspaces measured in the ℓ2 norm, but does not consider the actual computation of eigenvectors. Here we address the convergence of subspace iteration when distances are measured in the ℓ2 norm and provide deterministic bounds. We complement our analysis with a practical stopping criterion and demonstrate its applicability via numerical experiments. Our results show that one can get comparable performance on downstream tasks while requiring fewer iterations, thereby saving substantial computational time.

We study private synthetic data generation for query release, where the goal is to construct a sanitized version of a sensitive dataset, subject to differential privacy, that approximately preserves the answers to a large collection of statistical queries. We first present an algorithmic framework that unifies a long line of iterative algorithms in the literature. Under this framework, we propose two new methods. The first method, private entropy projection (PEP), can be viewed as an advanced variant of MWEM that adaptively reuses past query measurements to boost accuracy. Our second method, generative networks with the exponential mechanism (GEM), circumvents computational bottlenecks in algorithms such as MWEM and PEP by optimizing over generative models parameterized by neural networks, which capture a rich family of distributions while enabling fast gradient-based optimization. We demonstrate that PEP and GEM empirically outperform existing algorithms. Furthermore, we show that GEM nicely incorporates prior information from public data while overcoming limitations of PMW^Pub, the existing state-of-the-art method that also leverages public data.

A common method of attacking deep learning models is through adversarial attacks, which occur when an attacker specifically modifies the input of a model to produce an incorrect result. Adversarial attacks have been deeply investigated in the image domain; however, there is less research in the time-series domain and very little for forecasting financial data. To address these concerns, this study aims to build upon previous research on adversarial attacks for time-series data by introducing two new slope-based methods aimed to alter the trends of the predicted stock forecast generated by an N-HiTS model. Compared to the normal N-HiTS predictions, the two new slope-based methods, the General Slope Attack and Least-Squares Slope Attack, can manipulate N-HiTS predictions by doubling the slope. These new slope attacks can bypass standard security mechanisms, such as a discriminator that filters real and perturbed inputs, reducing a 4-layered CNN's specificity to 28% and accuracy to 57%. Furthermore, the slope based methods were incorporated into a GAN architecture as a means of generating realistic synthetic data, while simultaneously fooling the model. Finally, this paper also proposes a sample malware designed to inject an adversarial attack in the model inference library, proving that ML-security research should not only focus on making the model safe, but also securing the entire pipeline.

In this paper, we utilize the emerging idea of "coded computation" to design a novel error-correcting-code inspired technique for solving linear inverse problems under specific iterative

CoLA and discuss modifications to improve lower precision performance. In Appendix D we expand on the details of the experiments in the main text. We now present the linear algebra identities that we use to exploit structure in CoLA. I null Finally, for sum we have the Woodbury identity and its variants. Besides the compositional operators, we have some rules for some special operators.