Variational Quantum Circuits (VQCs) offer a novel pathway for quantum machine learning, yet their practical application is hindered by inherent limitations such as constrained linear expressivity, optimization challenges, and acute sensitivity to quantum hardware noise. This work introduces VQC-MLPNet, a scalable and robust hybrid quantum-classical architecture designed to overcome these obstacles. By innovatively employing quantum circuits to dynamically generate parameters for classical Multi-Layer Perceptrons (MLPs) via amplitude encoding and parameterized quantum operations, VQC-MLPNet substantially expands representation capabilities and augments training stability. We provide rigorous theoretical guarantees via statistical learning techniques and Neural Tangent Kernel analysis, explicitly deriving upper bounds on approximation, uniform deviation, and optimization errors. These theoretical insights demonstrate exponential improvements in representation capacity relative to quantum circuit depth and the number of qubits, providing clear computational advantages over standalone quantum circuits and existing hybrid quantum architectures. Our theoretical claims are empirically corroborated through extensive experiments, including classifying semiconductor quantum-dot charge states and predicting genomic transcription factor binding sites, demonstrating resilient performance even under realistic IBM quantum noise simulations. This research establishes a theoretically sound and practically robust framework, advancing the frontiers of quantum-enhanced learning for unconventional computing paradigms in the Noisy Intermediate-Scale Quantum era and beyond.

We propose a meta-learning method for learning from multiple noisy annotators. In many applications such as crowdsourcing services, labels for supervised learning are given by multiple annotators. Since the annotators have different skills or biases, given labels can be noisy. To learn accurate classifiers, existing methods require many noisy annotated data. However, sufficient data might be unavailable in practice. To overcome the lack of data, the proposed method uses labeled data obtained in different but related tasks. The proposed method embeds each example in tasks to a latent space by using a neural network and constructs a probabilistic model for learning a task-specific classifier while estimating annotators' abilities on the latent space. This neural network is meta-learned to improve the expected test classification performance when the classifier is adapted to a given small amount of annotated data. This classifier adaptation is performed by maximizing the posterior probability via the expectation-maximization (EM) algorithm. Since each step in the EM algorithm is easily computed as a closed-form and is differentiable, the proposed method can efficiently backpropagate the loss through the EM algorithm to meta-learn the neural network. We show the effectiveness of our method with real-world datasets with synthetic noise and real-world crowdsourcing datasets.

Density regression models allow a comprehensive understanding of data by modeling the complete conditional probability distribution. While flexible estimation approaches such as normalizing flows (NF) work particularly well in multiple dimensions, interpreting the input-output relationship of such models is often difficult, due to the black-box character of deep learning models. In contrast, existing statistical methods for multivariate outcomes such as multivariate conditional transformation models (MCTM) are restricted in flexibility and are often not expressive enough to represent complex multivariate probability distributions. In this paper, we combine MCTM with state-of-the-art and autoregressive NF to leverage the transparency of MCTM for modeling interpretable feature effects on the marginal distributions in the first step and the flexibility of neural-network-based NF techniques to account for complex and non-linear relationships in the joint data distribution. We demonstrate our method's versatility in various numerical experiments and compare it with MCTM and other NF models on both simulated and real-world data.

Air pollution has become a significant health risk in developing countries. While governments routinely publish air-quality index (AQI) data to track pollution, these values fail to capture the local reality, as sensors are often very sparse. In this paper, we address this gap by predicting AQI in 1 km^2 neighborhoods, using the example of AirDelhi dataset. Using Spatio-temporal GNNs we surpass existing works by 71.654 MSE a 79% reduction, even on unseen coordinates. New insights about AQI such as the existence of strong repetitive short-term patterns and changing spatial relations are also discovered. The code is available on GitHub.

Imagine trying to find a hidden k -vertex clique (fully connected subgraph) within an otherwise random n -vertex graph (network). While it is possible to find a hidden clique of size k log n by brute-force search, all known "fast" (polynomial-time) algorithms only work if the clique is much larger: k n . Is this an inherent limitation of fast algorithms or should we continue looking for a better one? Similar questions of computational complexity arise in many other statistical settings, such as community detection, clustering, and sparse PCA. While we lack the tools to prove definitively that fast algorithms require k n, this survey describes one sense in which we can prove this threshold is fundamental: all algorithms based on low-degree polynomials -- for instance, counting triangles in the graph would be a degree-3 polynomial -- provably fail (in an appropriate sense) when k n . Furthermore, these low-degree algorithms tend to capture the best tools in our algorithmic toolkit for problems of this style, so finding a fast algorithm for k n would seem to require a major breakthrough or may simply be impossible. This provides a lens for predicting and explaining the limitations of fast algorithms across many different settings.

Diffusion bridges are a promising class of deep-learning methods for sampling from unnormalized distributions. Recent works show that the Log Variance (LV) loss consistently outperforms the reverse Kullback-Leibler (rKL) loss when using the reparametrization trick to compute rKL-gradients. While the on-policy LV loss yields identical gradients to the rKL loss when combined with the log-derivative trick for diffusion samplers with non-learnable forward processes, this equivalence does not hold for diffusion bridges or when diffusion coefficients are learned. Based on this insight we argue that for diffusion bridges the LV loss does not represent an optimization objective that can be motivated like the rKL loss via the data processing inequality. Our analysis shows that employing the rKL loss with the log-derivative trick (rKL-LD) does not only avoid these conceptual problems but also consistently outperforms the LV loss. Experimental results with different types of diffusion bridges on challenging benchmarks show that samplers trained with the rKL-LD loss achieve better performance. From a practical perspective we find that rKL-LD requires significantly less hyperparameter optimization and yields more stable training behavior.

We address the problem of causal effect estimation in the presence of hidden confounders, using nonparametric instrumental variable (IV) regression. A leading strategy employs spectral features - that is, learned features spanning the top eigensubspaces of the operator linking treatments to instruments. We derive a generalization error bound for a two-stage least squares estimator based on spectral features, and gain insights into the method's performance and failure modes. We show that performance depends on two key factors, leading to a clear taxonomy of outcomes. In a good scenario, the approach is optimal. This occurs with strong spectral alignment, meaning the structural function is well-represented by the top eigenfunctions of the conditional operator, coupled with this operator's slow eigenvalue decay, indicating a strong instrument. Performance degrades in a bad scenario: spectral alignment remains strong, but rapid eigenvalue decay (indicating a weaker instrument) demands significantly more samples for effective feature learning. Finally, in the ugly scenario, weak spectral alignment causes the method to fail, regardless of the eigenvalues' characteristics. Our synthetic experiments empirically validate this taxonomy.

Survival analysis is a fundamental tool for modeling time-to-event data in healthcare, engineering, and finance, where censored observations pose significant challenges. While traditional methods like the Beran estimator offer nonparametric solutions, they often struggle with the complex data structures and heavy censoring. This paper introduces three novel survival models, iSurvM (the imprecise Survival model based on Mean likelihood functions), iSurvQ (the imprecise Survival model based on the Quantiles of likelihood functions), and iSurvJ (the imprecise Survival model based on the Joint learning), that combine imprecise probability theory with attention mechanisms to handle censored data without parametric assumptions. The first idea behind the models is to represent censored observations by interval-valued probability distributions for each instance over time intervals between events moments. The second idea is to employ the kernel-based Nadaraya-Watson regression with trainable attention weights for computing the imprecise probability distribution over time intervals for the entire dataset. The third idea is to consider three decision strategies for training, which correspond to the proposed three models. Experiments on synthetic and real datasets demonstrate that the proposed models, especially iSurvJ, consistently outperform the Beran estimator from the accuracy and computational complexity points of view. Codes implementing the proposed models are publicly available.

This study conducts an empirical examination of MLP networks investigated through a rigorous methodical experimentation process involving three diverse datasets: TinyFace, Heart Disease, and Iris. Study Overview: The study includes three key methods: a) a baseline training using the default settings for the Multi-Layer Perceptron (MLP), b) feature selection using Genetic Algorithm (GA) based refinement c) Principal Component Analysis (PCA) based dimension reduction. The results show important information on how such techniques affect performance. While PCA had showed benefits in low-dimensional and noise-free datasets GA consistently increased accuracy in complex datasets by accurately identifying critical features. Comparison reveals that feature selection and dimensionality reduction play interdependent roles in enhancing MLP performance. The study contributes to the literature on feature engineering and neural network parameter optimization, offering practical guidelines for a wide range of machine learning tasks

-- In many nations, diabetes is becoming a significant health problem, and early identi - fication and control are crucial. Using machine learning algorithms to predict diabetes has yielded encouraging results. Using the Pima Indians Dia - betes dataset, this study attempts to evaluate the efficacy of several machine - learning methods for diabetes prediction. The collection includes infor - mation on 768 patients, such as their ages, BMIs, and glucose levels. The techniques assessed are Logistic Regression, Decision Tree, Random Forest, k - Nearest Neighbors, Naive Bayes, Support Vector Machine, Gradient Boosting, and Neural Network. The findings indicate that the Neural Network algorithm performed the best, with an accuracy of 78.57 The study implies that machine learning algorithms can aid diabetes prediction and be an efficient early detection tool. Diabetes is a chronic metabolic disease af - fecting millions worldwide and is a significant cause of morbidity and death [1]. High blood glucose levels characterize the disorder and can result in some complications, including cardiovascular disease, stroke, blindness, and amputations. To prevent or postpone com - plications, diabetes must be recognized and treated as soon as feasible; however, this can be challenging because symptoms may be mild or absent [2]. Machine learning (ML) is a subfield of artificial intelligence that comprises the de - velopment of algorithms that can learn from data and generate inferences or predictions without being explicitly programmed. ML algorithms are beneficial in several fields, in - cluding healthcare.