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 Statistical Learning



RVN Algorithm

#artificialintelligence

When we need to cluster a data set, the first couple of algorithms we might look into are K means, DB scan, or hierarchical clustering algorithm. Those classic clustering algorithms always treat each data point as a dot. However, those data points usually have size or boundary(bounding box) in real life. Ignoring the edge of points might cause further bias. RVN algorithm is a method that considers points and the bounding box of each point.


Passing-Bablok regression in SAS

#artificialintelligence

This article implements Passing-Bablok regression in SAS. Passing-Bablok regression is a one-variable regression technique that is used to compare measurements from different instruments or medical devices. The measurements of the two variables (X and Y) are both measured with errors. Consequently, you cannot use ordinary linear regression, which assumes that one variable (X) is measured without error. Passing-Bablok regression is a robust nonparametric regression method that does not make assumptions about the distribution of the expected values or the error terms in the model.


Phenotyping with Positive Unlabelled Learning for Genome-Wide Association Studies

arXiv.org Artificial Intelligence

Identifying phenotypes plays an important role in furthering our understanding of disease biology through practical applications within healthcare and the life sciences. The challenge of dealing with the complexities and noise within electronic health records (EHRs) has motivated applications of machine learning in phenotypic discovery. While recent research has focused on finding predictive subtypes for clinical decision support, here we instead focus on the noise that results in phenotypic misclassification, which can reduce a phenotypes ability to detect associations in genome-wide association studies (GWAS). We show that by combining anchor learning and transformer architectures into our proposed model, AnchorBERT, we are able to detect genomic associations only previously found in large consortium studies with 5$\times$ more cases. When reducing the number of controls available by 50\%, we find our model is able to maintain 40\% more significant genomic associations from the GWAS catalog compared to standard phenotype definitions. \keywords{Phenotyping \and Machine Learning \and Semi-Supervised \and Genetic Association Studies \and Biological Discovery}


FAST-PCA: A Fast and Exact Algorithm for Distributed Principal Component Analysis

arXiv.org Artificial Intelligence

Principal Component Analysis (PCA) is a fundamental data preprocessing tool in the world of machine learning. While PCA is often thought of as a dimensionality reduction method, the purpose of PCA is actually two-fold: dimension reduction and uncorrelated feature learning. Furthermore, the enormity of the dimensions and sample size in the modern day datasets have rendered the centralized PCA solutions unusable. In that vein, this paper reconsiders the problem of PCA when data samples are distributed across nodes in an arbitrarily connected network. While a few solutions for distributed PCA exist, those either overlook the uncorrelated feature learning aspect of the PCA, tend to have high communication overhead that makes them inefficient and/or lack `exact' or `global' convergence guarantees. To overcome these aforementioned issues, this paper proposes a distributed PCA algorithm termed FAST-PCA (Fast and exAct diSTributed PCA). The proposed algorithm is efficient in terms of communication and is proven to converge linearly and exactly to the principal components, leading to dimension reduction as well as uncorrelated features. The claims are further supported by experimental results.


Bayesian Optimisation for Active Monitoring of Air Pollution

arXiv.org Artificial Intelligence

Air pollution is one of the leading causes of mortality globally, resulting in millions of deaths each year. Efficient monitoring is important to measure exposure and enforce legal limits. New low-cost sensors can be deployed in greater numbers and in more varied locations, motivating the problem of efficient automated placement. Previous work suggests Bayesian optimisation is an appropriate method, but only considered a satellite data set, with data aggregated over all altitudes. It is ground-level pollution, that humans breathe, which matters most. We improve on those results using hierarchical models and evaluate our models on urban pollution data in London to show that Bayesian optimisation can be successfully applied to the problem.


Accelerating Non-Negative and Bounded-Variable Linear Regression Algorithms with Safe Screening

arXiv.org Machine Learning

Non-negative and bounded-variable linear regression problems arise in a variety of applications in machine learning and signal processing. In this paper, we propose a technique to accelerate existing solvers for these problems by identifying saturated coordinates in the course of iterations. This is akin to safe screening techniques previously proposed for sparsity-regularized regression problems. The proposed strategy is provably safe as it provides theoretical guarantees that the identified coordinates are indeed saturated in the optimal solution. Experimental results on synthetic and real data show compelling accelerations for both non-negative and bounded-variable problems.


Reducing Overconfidence Predictions for Autonomous Driving Perception

arXiv.org Artificial Intelligence

In state-of-the-art deep learning for object recognition, SoftMax and Sigmoid functions are most commonly employed as the predictor outputs. Such layers often produce overconfident predictions rather than proper probabilistic scores, which can thus harm the decision-making of `critical' perception systems applied in autonomous driving and robotics. Given this, the experiments in this work propose a probabilistic approach based on distributions calculated out of the Logit layer scores of pre-trained networks. We demonstrate that Maximum Likelihood (ML) and Maximum a-Posteriori (MAP) functions are more suitable for probabilistic interpretations than SoftMax and Sigmoid-based predictions for object recognition. We explore distinct sensor modalities via RGB images and LiDARs (RV: range-view) data from the KITTI and Lyft Level-5 datasets, where our approach shows promising performance compared to the usual SoftMax and Sigmoid layers, with the benefit of enabling interpretable probabilistic predictions. Another advantage of the approach introduced in this paper is that the ML and MAP functions can be implemented in existing trained networks, that is, the approach benefits from the output of the Logit layer of pre-trained networks. Thus, there is no need to carry out a new training phase since the ML and MAP functions are used in the test/prediction phase.


Random Feature Amplification: Feature Learning and Generalization in Neural Networks

arXiv.org Machine Learning

In this work, we provide a characterization of the feature-learning process in two-layer ReLU networks trained by gradient descent on the logistic loss following random initialization. We consider data with binary labels that are generated by an XOR-like function of the input features. We permit a constant fraction of the training labels to be corrupted by an adversary. We show that, although linear classifiers are no better than random guessing for the distribution we consider, two-layer ReLU networks trained by gradient descent achieve generalization error close to the label noise rate, refuting the conjecture of Malach and Shalev-Shwartz that 'deeper is better only when shallow is good'. We develop a novel proof technique that shows that at initialization, the vast majority of neurons function as random features that are only weakly correlated with useful features, and the gradient descent dynamics 'amplify' these weak, random features to strong, useful features.


A Statistical Learning View of Simple Kriging

arXiv.org Machine Learning

In the Big Data era, with the ubiquity of geolocation sensors in particular, massive datasets exhibiting a possibly complex spatial dependence structure are becoming increasingly available. In this context, the standard probabilistic theory of statistical learning does not apply directly and guarantees of the generalization capacity of predictive rules learned from such data are left to establish. We analyze here the simple Kriging task, the flagship problem in Geostatistics: the values of a square integrable random field $X=\{X_s\}_{s\in S}$, $S\subset \mathbb{R}^2$, with unknown covariance structure are to be predicted with minimum quadratic risk, based upon observing a single realization of the spatial process at a finite number of locations $s_1,\; \ldots,\; s_n$ in $S$. Despite the connection of this minimization problem with kernel ridge regression, establishing the generalization capacity of empirical risk minimizers is far from straightforward, due to the non i.i.d. nature of the spatial data $X_{s_1},\; \ldots,\; X_{s_n}$ involved. In this article, nonasymptotic bounds of order $O_{\mathbb{P}}(1/n)$ are proved for the excess risk of a plug-in predictive rule mimicking the true minimizer in the case of isotropic stationary Gaussian processes observed at locations forming a regular grid. These theoretical results, as well as the role played by the technical conditions required to establish them, are illustrated by various numerical experiments and hopefully pave the way for further developments in statistical learning based on spatial data.