These notes gather recent results on robust statistical learning theory. The goal is to stress the main principles underlying the construction and theoretical analysis of these estimators rather than provide an exhaustive account on this rapidly growing field. The notes are the basis of lectures given at the conference StatMathAppli 2019.

Automatic Machine Learning (Auto-ML) has attracted more and more attention in recent years, our work is to solve the problem of data drift, which means that the distribution of data will gradually change with the acquisition process, resulting in a worse performance of the auto-ML model. We construct our model based on GBDT, Incremental learning and full learning are used to handle with drift problem. Experiments show that our method performs well on the five data sets. Which shows that our method can effectively solve the problem of data drift and has robust performance.

Generating paraphrases from given sentences involves decoding words step by step from a large vocabulary. To learn a decoder, supervised learning which maximizes the likelihood of tokens always suffers from the exposure bias. Although both reinforcement learning (RL) and imitation learning (IL) have been widely used to alleviate the bias, the lack of direct comparison leads to only a partial image on their benefits. In this work, we present an empirical study on how RL and IL can help boost the performance of generating paraphrases, with the pointer-generator as a base model. Experiments on the benchmark datasets show that (1) imitation learning is constantly better than reinforcement learning; and (2) the pointer-generator models with imitation learning outperform the state-of-the-art methods with a large margin.

Aim: To review how machine learning (ML) is applied to imaging biomarkers in neuro-oncology, in particular for diagnosis, prognosis, and treatment response monitoring. Materials and Methods: The PubMed and MEDLINE databases were searched for articles published before September 2018 using relevant search terms. The search strategy focused on articles applying ML to high-grade glioma biomarkers for treatment response monitoring, prognosis, and prediction. Results: Magnetic resonance imaging (MRI) is typically used throughout the patient pathway because routine structural imaging provides detailed anatomical and pathological information and advanced techniques provide additional physiological detail. Using carefully chosen image features, ML is frequently used to allow accurate classification in a variety of scenarios. Rather than being chosen by human selection, ML also enables image features to be identified by an algorithm. Much research is applied to determining molecular profiles, histological tumour grade, and prognosis using MRI images acquired at the time that patients first present with a brain tumour. Differentiating a treatment response from a post-treatment-related effect using imaging is clinically important and also an area of active study (described here in one of two Special Issue publications dedicated to the application of ML in glioma imaging). Conclusion: Although pioneering, most of the evidence is of a low level, having been obtained retrospectively and in single centres. Studies applying ML to build neuro-oncology monitoring biomarker models have yet to show an overall advantage over those using traditional statistical methods. Development and validation of ML models applied to neuro-oncology require large, well-annotated datasets, and therefore multidisciplinary and multi-centre collaborations are necessary.

Remote Sensing Images from satellites have been used in various domains for detecting and understanding structures on the ground surface. In this work, satellite images were used for localizing parking spaces and vehicles in parking lots for a given parcel using an RCNN based Neural Network Architectures. Parcel shapefiles and raster images from USGS image archive were used for developing images for both training and testing. Feature Pyramid based Mask RCNN yields average class accuracy of 97.56% for both parking spaces and vehicles

Short-and-sparse deconvolution (SaSD) is the problem of extracting localized, recurring motifs in signals with spatial or temporal structure. Variants of this problem arise in applications such as image deblurring, microscopy, neural spike sorting, and more. The problem is challenging in both theory and practice, as natural optimization formulations are nonconvex. Moreover, practical deconvolution problems involve smooth motifs (kernels) whose spectra decay rapidly, resulting in poor conditioning and numerical challenges. This paper is motivated by recent theoretical advances, which characterize the optimization landscape of a particular nonconvex formulation of SaSD. This is used to derive a $provable$ algorithm which exactly solves certain non-practical instances of the SaSD problem. We leverage the key ideas from this theory (sphere constraints, data-driven initialization) to develop a $practical$ algorithm, which performs well on data arising from a range of application areas. We highlight key additional challenges posed by the ill-conditioning of real SaSD problems, and suggest heuristics (acceleration, continuation, reweighting) to mitigate them. Experiments demonstrate both the performance and generality of the proposed method.

We analyze the classical EM algorithm for parameter estimation in the symmetric two-component Gaussian mixtures in $d$ dimensions. We show that, even in the absence of any separation between components, provided that the sample size satisfies $n=\Omega(d \log^3 d)$, the randomly initialized EM algorithm converges to an estimate in at most $O(\sqrt{n})$ iterations with high probability, which is at most $O((\frac{d \log^3 n}{n})^{1/4})$ in Euclidean distance from the true parameter and within logarithmic factors of the minimax rate of $(\frac{d}{n})^{1/4}$. Both the nonparametric statistical rate and the sublinear convergence rate are direct consequences of the zero Fisher information in the worst case. Refined pointwise guarantees beyond worst-case analysis and convergence to the MLE are also shown under mild conditions. This improves the previous result of Balakrishnan et al \cite{BWY17} which requires strong conditions on both the separation of the components and the quality of the initialization, and that of Daskalakis et al \cite{DTZ17} which requires sample splitting and restarting the EM iteration.

Clustering is the prototypical unsupervised learning activity which consists in identifying cohesive and well-differentiated groups of records in data. A data set is clusterable if such groups exist; however, due to the variety in data distributions and the inadequate formalization of certain basic notions of clustering, determining data clusterability before applying specific clustering algorithms is a difficult task. Evaluating data clusterability before the application of clustering algorithms can be very helpful because clustering algorithms are expensive. However, many such evaluations are impractical because they are NPhard, as shown in [4]. Other notions define data as clusterable when the minimum between-cluster separation is greater than the maximum intra-cluster distance [13], or when each element is closer to all elements in its cluster than to all other data [7].

Low-dimensional embeddings of knowledge graphs and behavior graphs have proved remarkably powerful in varieties of tasks, from predicting unobserved edges between entities to content recommendation. The two types of graphs can contain distinct and complementary information for the same entities/nodes. However, previous works focus either on knowledge graph embedding or behavior graph embedding while few works consider both in a unified way. Here we present BEM , a Bayesian framework that incorporates the information from knowledge graphs and behavior graphs. To be more specific, BEM takes as prior the pre-trained embeddings from the knowledge graph, and integrates them with the pre-trained embeddings from the behavior graphs via a Bayesian generative model. BEM is able to mutually refine the embeddings from both sides while preserving their own topological structures. To show the superiority of our method, we conduct a range of experiments on three benchmark datasets: node classification, link prediction, triplet classification on two small datasets related to Freebase, and item recommendation on a large-scale e-commerce dataset.

A widely applicable Bayesian information criterion (Watanabe, 2013) is applicable for both regular and singular models in the model selection problem. This criterion tends to overestimate the log marginal likelihood. We identify an overestimating term of a widely applicable Bayesian information criterion. Adjustment of the term gives an asymptotically unbiased estimator of the leading two terms of asymptotic expansion of the log marginal likelihood. In numerical experiments on regular and singular models, the adjustment resulted in smaller bias than the original criterion.