When the probability distribution P(X, Y) is known, the optimal classifier, leading to the minimum misclassification rate, is given by the Maximum A-posteriori Probability (MAP) decision rule. However, in practice, estimating the complete joint distribution P(X, Y) is computationally and statistically impossible for large values of d. Therefore, an alternative approach is to first estimate some low order marginals of the joint probability distribution P(X, Y) and then design the classifier based on the estimated low order marginals. This approach is also helpful when the complete training data instances are not available due to privacy concerns. In this work, we consider the problem of finding the optimum classifier based on some estimated low order marginals of (X, Y).

One approach to improving the running time of kernel-based methods is to build a small sketch of the kernel matrix and use it in lieu of the full matrix in the machine learning task of interest. Here, we describe a version of this approach that comes with running time guarantees as well as improved guarantees on its statistical performance. By extending the notion of statistical leverage scores to the setting of kernel ridge regression, we are able to identify a sampling distribution that reduces the size of the sketch (i.e., the required number of columns to be sampled) to the effective dimensionality of the problem. This latter quantity is often much smaller than previous bounds that depend on the maximal degrees of freedom. We give an empirical evidence supporting this fact. Our second contribution is to present a fast algorithm to quickly compute coarse approximations to these scores in time linear in the number of samples.

This paper proposes a framework for learning features that are robust to data variation, which is particularly important when only a limited number of training samples are available. The framework makes it possible to tradeoff the discriminative value of learned features against the generalization error of the learning algorithm. Robustness is achieved by encouraging the transform that maps data to features to be a local isometry. This geometric property is shown to improve (K, ɛ)-robustness, thereby providing theoretical justification for reductions in generalization error observed in experiments. The proposed optimization framework is used to train standard learning algorithms such as deep neural networks. Experimental results obtained on benchmark datasets, such as labeled faces in the wild, demonstrate the value of being able to balance discrimination and robustness.

The F-measure is an important and commonly used performance metric for binary prediction tasks. By combining precision and recall into a single score, it avoids disadvantages of simple metrics like the error rate, especially in cases of imbalanced class distributions. The problem of optimizing the F-measure, that is, of developing learning algorithms that perform optimally in the sense of this measure, has recently been tackled by several authors. In this paper, we study the problem of F-measure maximization in the setting of online learning. We propose an efficient online algorithm and provide a formal analysis of its convergence properties. Moreover, first experimental results are presented, showing that our method performs well in practice.

Learning the structure of a probabilistic graphical models is a well studied problem in the machine learning community due to its importance in many applications. Current approaches are mainly focused on learning the structure under restrictive parametric assumptions, which limits the applicability of these methods. In this paper, we study the problem of estimating the structure of a probabilistic graphical model without assuming a particular parametric model. We consider probabilities that are members of an infinite dimensional exponential family [4], which is parametrized by a reproducing kernel Hilbert space (RKHS) H and its kernel k. One difficulty in learning nonparametric densities is the evaluation of the normalizing constant. In order to avoid this issue, our procedure minimizes the penalized score matching objective [10, 11]. We show how to efficiently minimize the proposed objective using existing group lasso solvers. Furthermore, we prove that our procedure recovers the graph structure with high-probability under mild conditions. Simulation studies illustrate ability of our procedure to recover the true graph structure without the knowledge of the data generating process.

We consider the estimation of sparse graphical models that characterize the dependency structure of high-dimensional tensor-valued data. To facilitate the estimation of the precision matrix corresponding to each way of the tensor, we assume the data follow a tensor normal distribution whose covariance has a Kronecker product structure. The penalized maximum likelihood estimation of this model involves minimizing a non-convex objective function. In spite of the non-convexity of this estimation problem, we prove that an alternating minimization algorithm, which iteratively estimates each sparse precision matrix while fixing the others, attains an estimator with the optimal statistical rate of convergence as well as consistent graph recovery. Notably, such an estimator achieves estimation consistency with only one tensor sample, which is unobserved in previous work. Our theoretical results are backed by thorough numerical studies.

Natural language processing models have experienced a significant upsurge in recent years, with numerous applications being built upon them. Many of these applications require fine-tuning generic base models on customized, proprietary datasets. This fine-tuning data is especially likely to contain personal or sensitive information about individuals, resulting in increased privacy risk. Membership inference attacks are the most commonly employed attack to assess the privacy leakage of a machine learning model. However, limited research is available on the factors that affect the vulnerability of language models to this kind of attack, or on the applicability of different defense strategies in the language domain. We provide the first systematic review of the vulnerability of fine-tuned large language models to membership inference attacks, the various factors that come into play, and the effectiveness of different defense strategies. We find that some training methods provide significantly reduced privacy risk, with the combination of differential privacy and low-rank adaptors achieving the best privacy protection against these attacks.

Diffusion models have advanced unsupervised anomaly detection by improving the transformation of pathological images into pseudo-healthy equivalents. Nonetheless, standard approaches may compromise critical information during pathology removal, leading to restorations that do not align with unaffected regions in the original scans. Such discrepancies can inadvertently increase false positive rates and reduce specificity, complicating radiological evaluations. This paper introduces Temporal Harmonization for Optimal Restoration (THOR), which refines the de-noising process by integrating implicit guidance through temporal anomaly maps. THOR aims to preserve the integrity of healthy tissue in areas unaffected by pathology. Comparative evaluations show that THOR surpasses existing diffusion-based methods in detecting and segmenting anomalies in brain MRIs and wrist X-rays.

Within recent years, generative AI, such as large language models, has undergone rapid development. As these models become increasingly available to the public, concerns arise about perpetuating and amplifying harmful biases in applications. Gender stereotypes can be harmful and limiting for the individuals they target, whether they consist of misrepresentation or discrimination. Recognizing gender bias as a pervasive societal construct, this paper studies how to uncover and quantify the presence of gender biases in generative language models. In particular, we derive generative AI analogues of three well-known non-discrimination criteria from classification, namely independence, separation and sufficiency. To demonstrate these criteria in action, we design prompts for each of the criteria with a focus on occupational gender stereotype, specifically utilizing the medical test to introduce the ground truth in the generative AI context. Our results address the presence of occupational gender bias within such conversational language models.

Anomaly detection in dynamic graphs presents a significant challenge due to the temporal evolution of graph structures and attributes. The conventional approaches that tackle this problem typically employ an unsupervised learning framework, capturing normality patterns with exclusive normal data during training and identifying deviations as anomalies during testing. However, these methods face critical drawbacks: they either only depend on proxy tasks for general representation without directly pinpointing normal patterns, or they neglect to differentiate between spatial and temporal normality patterns, leading to diminished efficacy in anomaly detection. To address these challenges, we introduce a novel Spatial-Temporal memories-enhanced graph autoencoder (STRIPE). Initially, STRIPE employs Graph Neural Networks (GNNs) and gated temporal convolution layers to extract spatial features and temporal features, respectively. Then STRIPE incorporates separate spatial and temporal memory networks, which capture and store prototypes of normal patterns, thereby preserving the uniqueness of spatial and temporal normality. After that, through a mutual attention mechanism, these stored patterns are then retrieved and integrated with encoded graph embeddings. Finally, the integrated features are fed into the decoder to reconstruct the graph streams which serve as the proxy task for anomaly detection. This comprehensive approach not only minimizes reconstruction errors but also refines the model by emphasizing the compactness and distinctiveness of the embeddings in relation to the nearest memory prototypes. Through extensive testing, STRIPE has demonstrated a superior capability to discern anomalies by effectively leveraging the distinct spatial and temporal dynamics of dynamic graphs, significantly outperforming existing methodologies, with an average improvement of 15.39% on AUC values.