Vinayak Pathak

Shiqi Xu, Xiang Dai, Xi Yang et al.

We report Tensorial Tomographic Differential Phase-Contrast microscopy (T2DPC), a quantitative label-free tomographic imaging method for simultaneous measurement of phase and anisotropy. T2DPC extends differential phase-contrast microscopy, a quantitative phase imaging technique, to highlight the vectorial nature of light. The method solves for permittivity tensor of anisotropic samples from intensity measurements acquired with a standard microscope equipped with an LED matrix, a circular polarizer, and a polarization-sensitive camera. We demonstrate accurate volumetric reconstructions of refractive index, birefringence, and orientation for various validation samples, and show that the reconstructed polarization structures of a biological specimen are predictive of pathology.

Hassan Ashtiani, Vinayak Pathak, Ruth Urner

We initiate the study of tolerant adversarial PAC-learning with respect to metric perturbation sets. In adversarial PAC-learning, an adversary is allowed to replace a test point $x$ with an arbitrary point in a closed ball of radius $r$ centered at $x$. In the tolerant version, the error of the learner is compared with the best achievable error with respect to a slightly larger perturbation radius $(1+γ)r$. This simple tweak helps us bridge the gap between theory and practice and obtain the first PAC-type guarantees for algorithmic techniques that are popular in practice. Our first result concerns the widely-used ``perturb-and-smooth'' approach for adversarial learning. For perturbation sets with doubling dimension $d$, we show that a variant of these approaches PAC-learns any hypothesis class $\mathcal{H}$ with VC-dimension $v$ in the $γ$-tolerant adversarial setting with $O\left(\frac{v(1+1/γ)^{O(d)}}{\varepsilon}\right)$ samples. This is in contrast to the traditional (non-tolerant) setting in which, as we show, the perturb-and-smooth approach can provably fail. Our second result shows that one can PAC-learn the same class using $\widetilde{O}\left(\frac{d.v\log(1+1/γ)}{\varepsilon^2}\right)$ samples even in the agnostic setting. This result is based on a novel compression-based algorithm, and achieves a linear dependence on the doubling dimension as well as the VC-dimension. This is in contrast to the non-tolerant setting where there is no known sample complexity upper bound that depend polynomially on the VC-dimension.

Hassan Ashtiani, Vinayak Pathak, Ruth Urner

Adversarially robust PAC learning has proved to be challenging, with the currently best known learners [Montasser et al., 2021a] relying on improper methods based on intricate compression schemes, resulting in sample complexity exponential in the VC-dimension. A series of follow up work considered a slightly relaxed version of the problem called adversarially robust learning with tolerance [Ashtiani et al., 2023, Bhattacharjee et al., 2023, Raman et al., 2024] and achieved better sample complexity in terms of the VC-dimension. However, those algorithms were either improper and complex, or required additional assumptions on the hypothesis class H. We prove, for the first time, the existence of a simpler learner that achieves a sample complexity linear in the VC-dimension without requiring additional assumptions on H. Even though our learner is improper, it is "almost proper" in the sense that it outputs a hypothesis that is "similar" to a hypothesis in H. We also use the ideas from our algorithm to construct a semi-supervised learner in the tolerant setting. This simple algorithm achieves comparable bounds to the previous (non-tolerant) semi-supervised algorithm of Attias et al. [2022a], but avoids the use of intricate subroutines from previous works, and is "almost proper."

Xing Yao, Vinayak Pathak, Haoran Xi et al.

This work demonstrates a multi-lens microscopic imaging system that overlaps multiple independent fields of view on a single sensor for high-efficiency automated specimen analysis. Automatic detection, classification and counting of various morphological features of interest is now a crucial component of both biomedical research and disease diagnosis. While convolutional neural networks (CNNs) have dramatically improved the accuracy of counting cells and sub-cellular features from acquired digital image data, the overall throughput is still typically hindered by the limited space-bandwidth product (SBP) of conventional microscopes. Here, we show both in simulation and experiment that overlapped imaging and co-designed analysis software can achieve accurate detection of diagnostically-relevant features for several applications, including counting of white blood cells and the malaria parasite, leading to multi-fold increase in detection and processing throughput with minimal reduction in accuracy.

Hassan Ashtiani, Vinayak Pathak, Ruth Urner

We formally study the problem of classification under adversarial perturbations from a learner's perspective as well as a third-party who aims at certifying the robustness of a given black-box classifier. We analyze a PAC-type framework of semi-supervised learning and identify possibility and impossibility results for proper learning of VC-classes in this setting. We further introduce a new setting of black-box certification under limited query budget, and analyze this for various classes of predictors and perturbation. We also consider the viewpoint of a black-box adversary that aims at finding adversarial examples, showing that the existence of an adversary with polynomial query complexity can imply the existence of a sample efficient robust learner.