Since annotating medical images for segmentation tasks commonly incurs expensive costs, it is highly desirable to design an annotation-efficient method to alleviate the annotation burden. Recently, contrastive learning has exhibited a great potential in learning robust representations to boost downstream tasks with limited labels. In medical imaging scenarios, ready-made meta labels (i.e., specific attribute information of medical images) inherently reveal semantic relationships among images, which have been used to define positive pairs in previous work. However, the multi-perspective semantics revealed by various meta labels are usually incompatible and can incur intractable "semantic contradiction" when combining different meta labels. In this paper, we tackle the issue of "semantic contradiction" in a gradient-guided manner using our proposed Gradient Mitigator method, which systematically unifies multi-perspective meta labels to enable a pre-trained model to attain a better high-level semantic recognition ability. Moreover, we emphasize that the fine-grained discrimination ability is vital for segmentation-oriented pre-training, and develop a novel method called Gradient Filter to dynamically screen pixel pairs with the most discriminating power based on the magnitude of gradients. Comprehensive experiments on four medical image segmentation datasets verify that our new method GCL: (1) learns informative image representations and considerably boosts segmentation performance with limited labels, and (2) shows promising generalizability on out-of-distribution datasets.

Gaussian graphical models are widely used to represent correlations among entities but remain vulnerable to data corruption. In this work, we introduce a modified trimmed-inner-product algorithm to robustly estimate the covariance in an online scenario even in the presence of arbitrary and adversarial data attacks. At each time step, data points, drawn nominally independently and identically from a multivariate Gaussian distribution, arrive. However, a certain fraction of these points may have been arbitrarily corrupted. We propose an online algorithm to estimate the sparse inverse covariance (i.e., precision) matrix despite this corruption. We provide the error-bound and convergence properties of the estimates to the true precision matrix under our algorithms.

Complex networks are used to model many real-world systems. However, the dimensionality of these systems can make them challenging to analyze. Dimensionality reduction techniques like POD can be used in such cases. However, these models are susceptible to perturbations in the input data. We propose an algorithmic framework that combines techniques from pattern recognition (PR) and stochastic filtering theory to enhance the output of such models. The results of our study show that our method can improve the accuracy of the surrogate model under perturbed inputs. Deep Neural Networks (DNNs) are susceptible to adversarial attacks. However, recent research has revealed that Neural Ordinary Differential Equations (neural ODEs) exhibit robustness in specific applications. We benchmark our algorithmic framework with the neural ODE-based approach as a reference.

As machine learning becomes more widely used, the need to study its implications in security and privacy becomes more urgent. Although the body of work in privacy has been steadily growing over the past few years, research on the privacy aspects of machine learning has received less focus than the security aspects. Our contribution in this research is an analysis of more than 40 papers related to privacy attacks against machine learning that have been published during the past seven years. We propose an attack taxonomy, together with a threat model that allows the categorization of different attacks based on the adversarial knowledge, and the assets under attack. An initial exploration of the causes of privacy leaks is presented, as well as a detailed analysis of the different attacks. Finally, we present an overview of the most commonly proposed defenses and a discussion of the open problems and future directions identified during our analysis.

The problem of recovering a signal $\boldsymbol{x} \in \mathbb{R}^n$ from a quadratic system $\{y_i=\boldsymbol{x}^\top\boldsymbol{A}_i\boldsymbol{x},\ i=1,\ldots,m\}$ with full-rank matrices $\boldsymbol{A}_i$ frequently arises in applications such as unassigned distance geometry and sub-wavelength imaging. With i.i.d. standard Gaussian matrices $\boldsymbol{A}_i$, this paper addresses the high-dimensional case where $m\ll n$ by incorporating prior knowledge of $\boldsymbol{x}$. First, we consider a $k$-sparse $\boldsymbol{x}$ and introduce the thresholded Wirtinger flow (TWF) algorithm that does not require the sparsity level $k$. TWF comprises two steps: the spectral initialization that identifies a point sufficiently close to $\boldsymbol{x}$ (up to a sign flip) when $m=O(k^2\log n)$, and the thresholded gradient descent (with a good initialization) that produces a sequence linearly converging to $\boldsymbol{x}$ with $m=O(k\log n)$ measurements. Second, we explore the generative prior, assuming that $\boldsymbol{x}$ lies in the range of an $L$-Lipschitz continuous generative model with $k$-dimensional inputs in an $\ell_2$-ball of radius $r$. We develop the projected gradient descent (PGD) algorithm that also comprises two steps: the projected power method that provides an initial vector with $O\big(\sqrt{\frac{k \log L}{m}}\big)$ $\ell_2$-error given $m=O(k\log(Lnr))$ measurements, and the projected gradient descent that refines the $\ell_2$-error to $O(\delta)$ at a geometric rate when $m=O(k\log\frac{Lrn}{\delta^2})$. Experimental results corroborate our theoretical findings and show that: (i) our approach for the sparse case notably outperforms the existing provable algorithm sparse power factorization; (ii) leveraging the generative prior allows for precise image recovery in the MNIST dataset from a small number of quadratic measurements.

In recent years, a certain type of problems have become of interest where one wants to query a trained classifier. Specifically, one wants to find the closest instance to a given input instance such that the classifier's predicted label is changed in a desired way. Examples of these ``inverse classification'' problems are counterfactual explanations, adversarial examples and model inversion. All of them are fundamentally optimization problems over the input instance vector involving a fixed classifier, and it is of interest to achieve a fast solution for interactive or real-time applications. We focus on solving this problem efficiently for two of the most widely used classifiers: logistic regression and softmax classifiers. Owing to special properties of these models, we show that the optimization can be solved in closed form for logistic regression, and iteratively but extremely fast for the softmax classifier. This allows us to solve either case exactly (to nearly machine precision) in a runtime of milliseconds to around a second even for very high-dimensional instances and many classes.

We present TabPFN, a trained Transformer that can do supervised classification for small tabular datasets in less than a second, needs no hyperparameter tuning and is competitive with state-of-the-art classification methods. TabPFN performs in-context learning (ICL), it learns to make predictions using sequences of labeled examples (x, f(x)) given in the input, without requiring further parameter updates. TabPFN is fully entailed in the weights of our network, which accepts training and test samples as a set-valued input and yields predictions for the entire test set in a single forward pass. TabPFN is a Prior-Data Fitted Network (PFN) and is trained offline once, to approximate Bayesian inference on synthetic datasets drawn from our prior. This prior incorporates ideas from causal reasoning: It entails a large space of structural causal models with a preference for simple structures. On the 18 datasets in the OpenML-CC18 suite that contain up to 1 000 training data points, up to 100 purely numerical features without missing values, and up to 10 classes, we show that our method clearly outperforms boosted trees and performs on par with complex state-of-the-art AutoML systems with up to 230$\times$ speedup. This increases to a 5 700$\times$ speedup when using a GPU. We also validate these results on an additional 67 small numerical datasets from OpenML. We provide all our code, the trained TabPFN, an interactive browser demo and a Colab notebook at https://github.com/automl/TabPFN.

Offline change point detection retrospectively locates change points in a time series. Many nonparametric methods that target i.i.d. mean and variance changes fail in the presence of nonlinear temporal dependence, and model based methods require a known, rigid structure. For the at most one change point problem, we propose use of a conceptor matrix to learn the characteristic dynamics of a baseline training window with arbitrary dependence structure. The associated echo state network acts as a featurizer of the data, and change points are identified from the nature of the interactions between the features and their relationship to the baseline state. This model agnostic method can suggest potential locations of interest that warrant further study. We prove that, under mild assumptions, the method provides a consistent estimate of the true change point, and quantile estimates are produced via a moving block bootstrap of the original data. The method is evaluated with clustering metrics and Type 1 error control on simulated data, and applied to publicly available neural data from rats experiencing bouts of non-REM sleep prior to exploration of a radial maze. With sufficient spacing, the framework provides a simple extension to the sparse, multiple change point problem.

Clustering with outliers is one of the most fundamental problems in Computer Science. Given a set X of n points and two numbers k, m, the clustering with outliers aims to exclude m points from X and partition the remaining points into k clusters that minimizes a certain cost function. In this paper, we give a general approach for solving clustering with outliers, which results in a fixed-parameter tractable (FPT) algorithm in k and m—i.e., an algorithm with running time of the form f(k, m) · nO(1) for some function f—that almost matches the approximation ratio for its outlier-free counterpart. As a corollary, we obtain FPT approximation algorithms with optimal approximation ratios for k-Median and k-Means with outliers in general and Euclidean metrics. We also exhibit more applications of our approach to other variants of the problem that impose additional constraints on the clustering, such as fairness or matroid constraints.

Alzheimer's disease (AD) is the most prevalent neurodegenerative brain disorder, which results in significant cognitive impairments, especially in the elderly population. Cognitive impairments can manifest as a decline in various mental faculties, such as concentration, memory, and other higher-order cognitive abilities. These deficits can significantly impact an individual's capacity to comprehend information, acquire new knowledge, and communicate effectively. One of the affected activities due to cognitive impairments is handwriting. By analyzing different aspects of handwriting, including pressure, velocity, and spatial organization, researchers can detect subtle alterations that might indicate early-stage cognitive impairments, especially AD. Recently, several classical artificial intelligence (AI) approaches have been proposed for detecting AD in elderly individuals through handwriting analysis. However, advanced AI methods require more computational power as the size of the data increases. Additionally, diagnoses can be influenced by factors such as limited relevant classical vector space and correlations between features. Recent studies have shown that using quantum computing technologies in healthcare can not only address these problems but also accelerate complex data analysis and process large datasets more efficiently. In this study, we introduced a variational quantum classifier with fewer circuit elements to facilitate the early diagnosis of AD in elderly individuals based on handwriting data. We employed ZZFeatureMap for encoding features. To classify AD, a parameterized quantum circuit consisting of repeated Ry and Rz rotation gates, as well as CY and CZ two-qubit entangling gates, was designed and implemented. The proposed model achieved an accuracy of 0.75 in classifying AD.