We show how to achieve the notion of "multicalibration" from H\'ebert-Johnson et al. [2018] not just for means, but also for variances and other higher moments. Informally, it means that we can find regression functions which, given a data point, can make point predictions not just for the expectation of its label, but for higher moments of its label distribution as well-and those predictions match the true distribution quantities when averaged not just over the population as a whole, but also when averaged over an enormous number of finely defined subgroups. It yields a principled way to estimate the uncertainty of predictions on many different subgroups-and to diagnose potential sources of unfairness in the predictive power of features across subgroups. As an application, we show that our moment estimates can be used to derive marginal prediction intervals that are simultaneously valid as averaged over all of the (sufficiently large) subgroups for which moment multicalibration has been obtained.

We study the task of differentially private clustering. For several basic clustering problems, including Euclidean DensestBall, 1-Cluster, k-means, and k-median, we give efficient differentially private algorithms that achieve essentially the same approximation ratios as those that can be obtained by any non-private algorithm, while incurring only small additive errors. This improves upon existing efficient algorithms that only achieve some large constant approximation factors. Our results also imply an improved algorithm for the Sample and Aggregate privacy framework. Furthermore, we show that one of the tools used in our 1-Cluster algorithm can be employed to get a faster quantum algorithm for ClosestPair in a moderate number of dimensions.

Distance-based classification is among the most competitive classification methods for time series data. The most critical component of distance-based classification is the selected distance function. Past research has proposed various different distance metrics or measures dedicated to particular aspects of real-world time series data, yet there is an important aspect that has not been considered so far: Robustness against arbitrary data contamination. In this work, we propose a novel distance metric that is robust against arbitrarily "bad" contamination and has a worst-case computational complexity of $\mathcal{O}(n\log n)$. We formally argue why our proposed metric is robust, and demonstrate in an empirical evaluation that the metric yields competitive classification accuracy when applied in k-Nearest Neighbor time series classification.

With the increasing demands for privacy protection, many privacy-preserving machine learning systems were proposed in recent years. However, most of them cannot be put into production due to their slow training and inference speed caused by the heavy cost of homomorphic encryption and secure multiparty computation(MPC) methods. To circumvent this, I proposed a privacy definition which is suitable for large amount of data in machine learning tasks. Based on that, I showed that random transformations like linear transformation and random permutation can well protect privacy. Merging random transformations and arithmetic sharing together, I designed a framework for private machine learning with high efficiency and low computation cost.

Most existing metric learning methods focus on learning a similarity or distance measure relying on similar and dissimilar relations between sample pairs. However, pairs of samples cannot be simply identified as similar or dissimilar in many real-world applications, e.g., multi-label learning, label distribution learning. To this end, relation alignment metric learning (RAML) framework is proposed to handle the metric learning problem in those scenarios. But RAML framework uses SVR solvers for optimization. It can't learn positive semidefinite distance metric which is necessary in metric learning. In this paper, we propose two methds to overcame the weakness. Further, We carry out several experiments on the single-label classification, multi-label classification, label distribution learning to demonstrate the new methods achieves favorable performance against RAML framework.

We study the dynamics of optimization and the generalization properties of one-hidden layer neural networks with quadratic activation function in the over-parametrized regime where the layer width $m$ is larger than the input dimension $d$. We consider a teacher-student scenario where the teacher has the same structure as the student with a hidden layer of smaller width $m^*\le m$. We describe how the empirical loss landscape is affected by the number $n$ of data samples and the width $m^*$ of the teacher network. In particular we determine how the probability that there be no spurious minima on the empirical loss depends on $n$, $d$, and $m^*$, thereby establishing conditions under which the neural network can in principle recover the teacher. We also show that under the same conditions gradient descent dynamics on the empirical loss converges and leads to small generalization error, i.e. it enables recovery in practice. Finally we characterize the time-convergence rate of gradient descent in the limit of a large number of samples. These results are confirmed by numerical experiments.

But they are a few problems relating to using a traditional R CNN. Mainly that processing an image takes a lot of time. As the model is extracting 2000 regions to check. Prediction with the model takes around 40 seconds. A better version of R CNN was created by the same person.

CNN's have been extensively used to classify images. But to detect an object in an image and to draw bounding boxes around them is a tough problem to solve. To solve this problem, R-CNN algorithm was published in 2014. After R-CNN, many of its variants like Fast-R-CNN, Faster-R-CNN and Mask-R-CNN came which improvised the task of object detection. To understand the latest R-CNN variants, it is important to have a clear understanding of R-CNN.

Neuropsychiatric disorders are diagnosed based on behavioral criteria, which makes the diagnosis challenging. Objective biomarkers such as neuroimaging are needed, and when coupled with machine learning, can assist the diagnostic decision and increase its reliability. Sixty-four schizophrenia, 36 autism spectrum disorder (ASD), and 106 typically developing individuals were analyzed. FreeSurfer was used to obtain the data from the participant’s brain scans. Six classifiers were utilized to classify the subjects. Subsequently, 26 ultra-high risk for psychosis (UHR) and 17 first-episode psychosis (FEP) subjects were run through the trained classifiers. Lastly, the classifiers’ output of the patient groups was correlated with their clinical severity. All six classifiers performed relatively well to distinguish the subject groups, especially support vector machine (SVM) and Logistic regression (LR). Cortical thickness and subcortical volume feature groups were most useful for the classification. LR and SVM were highly consistent with clinical indices of ASD. When UHR and FEP groups were run with the trained classifiers, majority of the cases were classified as schizophrenia, none as ASD. Overall, SVM and LR were the best performing classifiers. Cortical thickness and subcortical volume were most useful for the classification, compared to surface area. LR, SVM, and DT’s output were clinically informative. The trained classifiers were able to help predict the diagnostic category of both UHR and FEP Individuals.

PCA provides valuable insights that reach beyond descriptive statistics and help to discover underlying patterns. Two PCA metrics indicate 1. how many components capture the largest share of variance (explained variance), and 2., which features correlate with the most important components (factor loading). These metrics crosscheck previous steps in the project work flow, such as data collection which then can be adjusted. As a shortcut and ready-to-use tool, I provide the function do_pca() which conducts a PCA for a prepared dataset to inspect its results within seconds in this notebook or this script. When a project structure resembles the one below, the prepared dataset is under scrutiny in the 4. step by looking at descriptive statistics. Among the most common ones are means, distributions and correlations taken across all observations or subgroups.