Calibrated confidence estimates obtained from neural networks are crucial, particularly for safety-critical applications such as autonomous driving or medical image diagnosis. However, although the task of confidence calibration has been investigated on classification problems, thorough investigations on object detection and segmentation problems are still missing. Therefore, we focus on the investigation of confidence calibration for object detection and segmentation models in this chapter. We introduce the concept of multivariate confidence calibration that is an extension of well-known calibration methods to the task of object detection and segmentation. This allows for an extended confidence calibration that is also aware of additional features such as bounding box/pixel position, shape information, etc. Furthermore, we extend the expected calibration error (ECE) to measure miscalibration of object detection and segmentation models. We examine several network architectures on MS COCO as well as on Cityscapes and show that especially object detection as well as instance segmentation models are intrinsically miscalibrated given the introduced definition of calibration. Using our proposed calibration methods, we have been able to improve calibration so that it also has a positive impact on the quality of segmentation masks as well.

Minimax optimization has served as the backbone of many machine learning (ML) problems. Although the convergence behavior of optimization algorithms has been extensively studied in the minimax settings, their generalization guarantees in stochastic minimax optimization problems, i.e., how the solution trained on empirical data performs on unseen testing data, have been relatively underexplored. A fundamental question remains elusive: What is a good metric to study generalization of minimax learners? In this paper, we aim to answer this question by first showing that primal risk, a universal metric to study generalization in minimization problems, which has also been adopted recently to study generalization in minimax ones, fails in simple examples. We thus propose a new metric to study generalization of minimax learners: the primal gap, defined as the difference between the primal risk and its minimum over all models, to circumvent the issues. Next, we derive generalization error bounds for the primal gap in nonconvex-concave settings. As byproducts of our analysis, we also solve two open questions: establishing generalization error bounds for primal risk and primal-dual risk, another existing metric that is only well-defined when the global saddle-point exists, in the strong sense, i.e., without strong concavity or assuming that the maximization and expectation can be interchanged, while either of these assumptions was needed in the literature. Finally, we leverage this new metric to compare the generalization behavior of two popular algorithms -- gradient descent-ascent (GDA) and gradient descent-max (GDMax) in stochastic minimax optimization.

Many recent problems in signal processing and machine learning such as compressed sensing, image restoration, matrix/tensor recovery, and non-negative matrix factorization can be cast as constrained optimization. Projected gradient descent is a simple yet efficient method for solving such constrained optimization problems. Local convergence analysis furthers our understanding of its asymptotic behavior near the solution, offering sharper bounds on the convergence rate compared to global convergence analysis. However, local guarantees often appear scattered in problem-specific areas of machine learning and signal processing. This manuscript presents a unified framework for the local convergence analysis of projected gradient descent in the context of constrained least squares. The proposed analysis offers insights into pivotal local convergence properties such as the conditions for linear convergence, the region of convergence, the exact asymptotic rate of convergence, and the bound on the number of iterations needed to reach a certain level of accuracy. To demonstrate the applicability of the proposed approach, we present a recipe for the convergence analysis of projected gradient descent and demonstrate it via a beginning-to-end application of the recipe on four fundamental problems, namely, linear equality-constrained least squares, sparse recovery, least squares with the unit norm constraint, and matrix completion.

The investigation of dynamical processes on networks has been one focus for the study of contagion processes. It has been demonstrated that contagions can be used to obtain information about the embedding of nodes in a Euclidean space. Specifically, one can use the activation times of threshold contagions to construct contagion maps as a manifold-learning approach. One drawback of contagion maps is their high computational cost. Here, we demonstrate that a truncation of the threshold contagions may considerably speed up the construction of contagion maps. Finally, we show that contagion maps may be used to find an insightful low-dimensional embedding for single-cell RNA-sequencing data in the form of cell-similarity networks and so reveal biological manifolds. Overall, our work makes the use of contagion maps as manifold-learning approaches on empirical network data more viable.

Since the start of your data scientist journey, you have been commonly accustomed with this machine learning algorithm. Linear Regression as it is the basic and foremost machine learning algorithm we generally start with while analysing different regression problems. As the word linear says, the linear relationship between input variables(x) with the dependent output variable(y). Basically the linear regression analysis performs the task of predicticting the output variable by modelling or finding relationships between the independent variables(x). And the approach of finding the best ouput is by fitting the predicted line towards the best fit line.

As statistical machine learning impacts several domain applications of major importance to the planet and society, ranging from healthcare to the environment, sophisticated approaches to estimation, proceeding in multiple stages, are being developed to overcome confounding factors and to address high-dimensional nuisance parameters (Peters et al., 2017). Orthogonal statistical learning (OSL), and its statistical estimation predecessor double machine learning (DML), have emerged as general frameworks for two-stage statistical machine learning in the presence of a nuisance component (Mackey et al., 2018; Liu et al., 2021; Nekipelov et al., 2022). The power of this framework can be illustrated on the task of assessing the causal effect of a treatment on an outcome of interest.

Making predictions robust is an important challenge. A separate challenge in federated learning (FL) is to reduce the number of communication rounds, particularly since doing so reduces performance in heterogeneous data settings. To tackle both issues, we take a Bayesian perspective on the problem of learning a global model. We show how the global predictive posterior can be approximated using client predictive posteriors. This is unlike other works which aggregate the local model space posteriors into the global model space posterior, and are susceptible to high approximation errors due to the posterior's high dimensional multimodal nature. In contrast, our method performs the aggregation on the predictive posteriors, which are typically easier to approximate owing to the low-dimensionality of the output space. We present an algorithm based on this idea, which performs MCMC sampling at each client to obtain an estimate of the local posterior, and then aggregates these in one round to obtain a global ensemble model. Through empirical evaluation on several classification and regression tasks, we show that despite using one round of communication, the method is competitive with other FL techniques, and outperforms them on heterogeneous settings. The code is publicly available at https://github.com/hasanmohsin/FedPredSpace_1Round.

Let's, start with what is OpenCV. OpenCV or Open Source Computer Vision Library is an open-source and free to use library under the Apache 2.0 license. OpenCV is mainly used for computer vision, image processing, and machine learning tasks. The library was originally developed by Intel in 1999. OpenCV supports a variety of languages like C, Python, Java, etc., and can be used on Windows, Linux, Android, and Mac OS.

In this work, we present local convergence analysis and a recovery guarantee for KSS, assuming In the UoS model, the goal of SC is to recover the data are generated by the semi-random underlying subspaces and cluster the unlabeled data union of subspaces model, where N points are points into the corresponding subspaces. To achieve randomly sampled from K 2 overlapping this goal, many algorithms have been proposed in subspaces. We show that if the initial assignment the past two decades, such as sparse subspace clustering of the KSS method lies within a neighborhood methods (Elhamifar & Vidal, 2013; Wang & Xu, of a true clustering, it converges at a 2013), low-rank representation-based methods (Liu et al., superlinear rate and finds the correct clustering 2012), thresholding-based methods (Heckel & Bölcskei, within Θ(loglogN) iterations with high probability.

We consider the problem of nonstochastic control with a sequence of quadratic losses, i.e., LQR control. We provide an efficient online algorithm that achieves an optimal dynamic (policy) regret of $\tilde{O}(\text{max}\{n^{1/3} \mathcal{TV}(M_{1:n})^{2/3}, 1\})$, where $\mathcal{TV}(M_{1:n})$ is the total variation of any oracle sequence of Disturbance Action policies parameterized by $M_1,...,M_n$ -- chosen in hindsight to cater to unknown nonstationarity. The rate improves the best known rate of $\tilde{O}(\sqrt{n (\mathcal{TV}(M_{1:n})+1)} )$ for general convex losses and we prove that it is information-theoretically optimal for LQR. Main technical components include the reduction of LQR to online linear regression with delayed feedback due to Foster and Simchowitz (2020), as well as a new proper learning algorithm with an optimal $\tilde{O}(n^{1/3})$ dynamic regret on a family of ``minibatched'' quadratic losses, which could be of independent interest.