量子计算有可能彻底改变和改变我们的生活和理解世界的方式。该审查旨在提供对量子计算的可访问介绍，重点是统计和数据分析中的应用。我们从介绍了了解量子计算所需的基本概念以及量子和经典计算之间的差异。我们描述了用作量子算法的构建块的核心量子子程序。然后，我们审查了一系列预期的量子算法，以便在统计和机器学习中提供计算优势。我们突出了将量子计算应用于统计问题的挑战和机遇，并讨论潜在的未来研究方向。

变异贝叶斯（VB）是机器学习和统计数据中的关键方法，是贝叶斯深度学习最近成功的基础。天然梯度是有效VB估计的重要组成部分，但在高维度上的计算量非常昂贵。我们提出了一种基于计算有效回归的自然梯度估计方法，并根据标准假设提供了收敛的保证。该方法使使用量子矩阵倒置可以进一步加速VB。我们证明问题设置满足了量子矩阵反转所需的条件以实现计算效率。该方法可与广泛的统计模型一起使用，不需要特殊用途或简化的变异分布。

In this paper, we propose a novel technique, namely INVALIDATOR, to automatically assess the correctness of APR-generated patches via semantic and syntactic reasoning. INVALIDATOR reasons about program semantic via program invariants while it also captures program syntax via language semantic learned from large code corpus using the pre-trained language model. Given a buggy program and the developer-patched program, INVALIDATOR infers likely invariants on both programs. Then, INVALIDATOR determines that a APR-generated patch overfits if: (1) it violates correct specifications or (2) maintains errors behaviors of the original buggy program. In case our approach fails to determine an overfitting patch based on invariants, INVALIDATOR utilizes a trained model from labeled patches to assess patch correctness based on program syntax. The benefit of INVALIDATOR is three-fold. First, INVALIDATOR is able to leverage both semantic and syntactic reasoning to enhance its discriminant capability. Second, INVALIDATOR does not require new test cases to be generated but instead only relies on the current test suite and uses invariant inference to generalize the behaviors of a program. Third, INVALIDATOR is fully automated. We have conducted our experiments on a dataset of 885 patches generated on real-world programs in Defects4J. Experiment results show that INVALIDATOR correctly classified 79% overfitting patches, accounting for 23% more overfitting patches being detected by the best baseline. INVALIDATOR also substantially outperforms the best baselines by 14% and 19% in terms of Accuracy and F-Measure, respectively.

Modern deep neural networks have achieved superhuman performance in tasks from image classification to game play. Surprisingly, these various complex systems with massive amounts of parameters exhibit the same remarkable structural properties in their last-layer features and classifiers across canonical datasets. This phenomenon is known as "Neural Collapse," and it was discovered empirically by Papyan et al. \cite{Papyan20}. Recent papers have theoretically shown the global solutions to the training network problem under a simplified "unconstrained feature model" exhibiting this phenomenon. We take a step further and prove the Neural Collapse occurrence for deep linear network for the popular mean squared error (MSE) and cross entropy (CE) loss. Furthermore, we extend our research to imbalanced data for MSE loss and present the first geometric analysis for Neural Collapse under this setting.

We present a Machine Learning (ML) study case to illustrate the challenges of clinical translation for a real-time AI-empowered echocardiography system with data of ICU patients in LMICs. Such ML case study includes data preparation, curation and labelling from 2D Ultrasound videos of 31 ICU patients in LMICs and model selection, validation and deployment of three thinner neural networks to classify apical four-chamber view. Results of the ML heuristics showed the promising implementation, validation and application of thinner networks to classify 4CV with limited datasets. We conclude this work mentioning the need for (a) datasets to improve diversity of demographics, diseases, and (b) the need of further investigations of thinner models to be run and implemented in low-cost hardware to be clinically translated in the ICU in LMICs. The code and other resources to reproduce this work are available at https://github.com/vital-ultrasound/ai-assisted-echocardiography-for-low-resource-countries.

Ensemble learning combines results from multiple machine learning models in order to provide a better and optimised predictive model with reduced bias, variance and improved predictions. However, in federated learning it is not feasible to apply centralised ensemble learning directly due to privacy concerns. Hence, a mechanism is required to combine results of local models to produce a global model. Most distributed consensus algorithms, such as Byzantine fault tolerance (BFT), do not normally perform well in such applications. This is because, in such methods predictions of some of the peers are disregarded, so a majority of peers can win without even considering other peers' decisions. Additionally, the confidence score of the result of each peer is not normally taken into account, although it is an important feature to consider for ensemble learning. Moreover, the problem of a tie event is often left un-addressed by methods such as BFT. To fill these research gaps, we propose PoSw (Proof of Swarm), a novel distributed consensus algorithm for ensemble learning in a federated setting, which was inspired by particle swarm based algorithms for solving optimisation problems. The proposed algorithm is theoretically proved to always converge in a relatively small number of steps and has mechanisms to resolve tie events while trying to achieve sub-optimum solutions. We experimentally validated the performance of the proposed algorithm using ECG classification as an example application in healthcare, showing that the ensemble learning model outperformed all local models and even the FL-based global model. To the best of our knowledge, the proposed algorithm is the first attempt to make consensus over the output results of distributed models trained using federated learning.

In the era of Internet of Things (IoT), network-wide anomaly detection is a crucial part of monitoring IoT networks due to the inherent security vulnerabilities of most IoT devices. Principal Components Analysis (PCA) has been proposed to separate network traffics into two disjoint subspaces corresponding to normal and malicious behaviors for anomaly detection. However, the privacy concerns and limitations of devices' computing resources compromise the practical effectiveness of PCA. We propose a federated PCA-based Grassmannian optimization framework that coordinates IoT devices to aggregate a joint profile of normal network behaviors for anomaly detection. First, we introduce a privacy-preserving federated PCA framework to simultaneously capture the profile of various IoT devices' traffic. Then, we investigate the alternating direction method of multipliers gradient-based learning on the Grassmann manifold to guarantee fast training and the absence of detecting latency using limited computational resources. Empirical results on the NSL-KDD dataset demonstrate that our method outperforms baseline approaches. Finally, we show that the Grassmann manifold algorithm is highly adapted for IoT anomaly detection, which permits drastically reducing the analysis time of the system. To the best of our knowledge, this is the first federated PCA algorithm for anomaly detection meeting the requirements of IoT networks.

Consider $n$ points independently sampled from a density $p$ of class $\mathcal{C}^2$ on a smooth compact $d$-dimensional sub-manifold $\mathcal{M}$ of $\mathbb{R}^m$, and consider the generator of a random walk visiting these points according to a transition kernel $K$. We study the almost sure uniform convergence of this operator to the diffusive Laplace-Beltrami operator when $n$ tends to infinity. This work extends known results of the past 15 years. In particular, our result does not require the kernel $K$ to be continuous, which covers the cases of walks exploring $k$NN-random and geometric graphs, and convergence rates are given. The distance between the random walk generator and the limiting operator is separated into several terms: a statistical term, related to the law of large numbers, is treated with concentration tools and an approximation term that we control with tools from differential geometry. The convergence of $k$NN Laplacians is detailed.

We study the multiclass classification problem where the features come from the mixture of time-homogeneous diffusions. Specifically, the classes are discriminated by their drift functions while the diffusion coefficient is common to all classes and unknown. In this framework, we build a plug-in classifier which relies on nonparametric estimators of the drift and diffusion functions. We first establish the consistency of our classification procedure under mild assumptions and then provide rates of cnvergence under different set of assumptions. Finally, a numerical study supports our theoretical findings.

Differentiable Search Indices (DSIs) encode a corpus of documents in the parameters of a model and use the same model to map queries directly to relevant document identifiers. Despite the strong performance of DSI models, deploying them in situations where the corpus changes over time is computationally expensive because reindexing the corpus requires re-training the model. In this work, we introduce DSI++, a continual learning challenge for DSI to incrementally index new documents while being able to answer queries related to both previously and newly indexed documents. Across different model scales and document identifier representations, we show that continual indexing of new documents leads to considerable forgetting of previously indexed documents. We also hypothesize and verify that the model experiences forgetting events during training, leading to unstable learning. To mitigate these issues, we investigate two approaches. The first focuses on modifying the training dynamics. Flatter minima implicitly alleviate forgetting, so we optimize for flatter loss basins and show that the model stably memorizes more documents (+12\%). Next, we introduce a generative memory to sample pseudo-queries for documents and supplement them during continual indexing to prevent forgetting for the retrieval task. Extensive experiments on novel continual indexing benchmarks based on Natural Questions (NQ) and MS MARCO demonstrate that our proposed solution mitigates forgetting by a significant margin. Concretely, it improves the average Hits@10 by $+21.1\%$ over competitive baselines for NQ and requires $6$ times fewer model updates compared to re-training the DSI model for incrementally indexing five corpora in a sequence.