Statistical Learning
Artificial Intelligence #3:kNN & Bayes Classification method
This can be thought of as the training set for the algorithm, though no explicit training step is required.by Sobhan N. What you'll learn Use k Nearest Neighbor classification method to classify datasets. Write your own code to make k Nearest Neighbor classification method by yourself. Use k Nearest Neighbor classification method to classify IRIS dataset. Use Naive Bayes classification method to classify datasets.
Distributed Estimation for Principal Component Analysis: a Gap-free Approach
Chen, Xi, Lee, Jason D., Li, He, Yang, Yun
The growing size of modern data sets brings many challenges to the existing statistical estimation approaches, which calls for new distributed methodologies. This paper studies distributed estimation for a fundamental statistical machine learning problem, principal component analysis (PCA). Despite the massive literature on top eigenvector estimation, much less is presented for the top-$L$-dim ($L > 1$) eigenspace estimation, especially in a distributed manner. We propose a novel multi-round algorithm for constructing top-$L$-dim eigenspace for distributed data. Our algorithm takes advantage of shift-and-invert preconditioning and convex optimization. Our estimator is communication-efficient and achieves a fast convergence rate. In contrast to the existing divide-and-conquer algorithm, our approach has no restriction on the number of machines. Theoretically, we establish a gap-free error bound and abandon the assumption on the sharp eigengap between the $L$-th and the ($L+1$)-th eigenvalues. Our distributed algorithm can be applied to a wide range of statistical problems based on PCA. In particular, this paper illustrates two important applications, principal component regression and single index model, where our distributed algorithm can be extended. Finally, We provide simulation studies to demonstrate the performance of the proposed distributed estimator.
A new hashing based nearest neighbors selection technique for big datasets
Tchaye-Kondi, Jude, Zhai, Yanlong, Zhu, Liehuang
KNN has the reputation to be the word simplest but efficient supervised learning algorithm used for either classification or regression. KNN prediction efficiency highly depends on the size of its training data but when this training data grows KNN suffers from slowness in making decisions since it needs to search nearest neighbors within the entire dataset at each decision making. This paper proposes a new technique that enables the selection of nearest neighbors directly in the neighborhood of a given observation. The proposed approach consists of dividing the data space into subcells of a virtual grid built on top of data space. The mapping between the data points and subcells is performed using hashing. When it comes to select the nearest neighbors of a given observation, we firstly identify the cell the observation belongs by using hashing, and then we look for nearest neighbors from that central cell and cells around it layer by layer. From our experiment performance analysis on publicly available datasets, our algorithm outperforms the original KNN in time efficiency with a prediction quality as good as that of KNN it also offers competitive performance with solutions like KDtree
Dynamic Decision Boundary for One-class Classifiers applied to non-uniformly Sampled Data
La Grassa, Riccardo, Gallo, Ignazio, Landro, Nicola
A typical issue in Pattern Recognition is the non-uniformly sampled data, which modifies the general performance and capability of machine learning algorithms to make accurate predictions. Generally, the data is considered non-uniformly sampled when in a specific area of data space, they are not enough, leading us to misclassification problems. This issue cut down the goal of the one-class classifiers decreasing their performance. In this paper, we propose a one-class classifier based on the minimum spanning tree with a dynamic decision boundary (OCdmst) to make good prediction also in the case we have non-uniformly sampled data. To prove the effectiveness and robustness of our approach we compare with the most recent one-class classifier reaching the state-of-the-art in most of them.
Long-tail learning with attributes
Samuel, Dvir, Atzmon, Yuval, Chechik, Gal
Learning to classify images with unbalanced class distributions is challenged by two effects: It is hard to learn tail classes that have few samples, and it is hard to adapt a single model to both richly-sampled and poorly-sampled classes. To address few-shot learning of tail classes, it is useful to fuse additional information in the form of semantic attributes and classify based on multi-modal information. Unfortunately, as we show below, unbalanced data leads to a "familiarity bias", where classifiers favor sample-rich classes. This bias and lack of calibrated predictions make it hard to fuse correctly information from multiple modalities like vision and attributes. Here we describe DRAGON, a novel modular architecture for long-tail learning designed to address these biases and fuse multi-modal information in face of unbalanced data. Our architecture is based on three classifiers: a vision expert, a semantic attribute expert that excels on the tail classes, and a debias-and-fuse module to combine their predictions. We present the first benchmark for long-tail learning with attributes and use it to evaluate DRAGON. DRAGON outperforms state-of-the-art long-tail learning models and Generalized Few-Shot-Learning with attributes (GFSL-a) models. DRAGON also obtains SoTA in some existing benchmarks for single-modality GFSL.
FairNN- Conjoint Learning of Fair Representations for Fair Decisions
Hu, Hongxin, Iosifidis, Vasileios, Liao, Wentong, Zhang, Hang, YingYang, Michael, Ntoutsi, Eirini, Rosenhahn, Bodo
In this paper, we propose FairNN a neural network that performs joint feature representation and classification for fairness-aware learning. Our approach optimizes a multi-objective loss function in which (a) learns a fair representation by suppressing protected attributes (b) maintains the information content by minimizing a reconstruction loss and (c) allows for solving a classification task in a fair manner by minimizing the classification error and respecting the equalized odds-based fairness regularizer. Our experiments on a variety of datasets demonstrate that such a joint approach is superior to separate treatment of unfairness in representation learning or supervised learning. Additionally, our regularizers can be adaptively weighted to balance the different components of the loss function, thus allowing for a very general framework for conjoint fair representation learning and decision making.
An information-geometric approach to feature extraction and moment reconstruction in dynamical systems
Das, Suddhasattwa, Giannakis, Dimitrios, Szรฉkely, Enikล
We propose a dimension reduction framework for feature extraction and moment reconstruction in dynamical systems that operates on spaces of probability measures induced by observables of the system rather than directly in the original data space of the observables themselves as in more conventional methods. Our approach is based on the fact that orbits of a dynamical system induce probability measures over the measurable space defined by (partial) observations of the system. We equip the space of these probability measures with a divergence, i.e., a distance between probability distributions, and use this divergence to define a kernel integral operator. The eigenfunctions of this operator create an orthonormal basis of functions that capture different timescales of the dynamical system. One of our main results shows that the evolution of the moments of the dynamics-dependent probability measures can be related to a time-averaging operator on the original dynamical system. Using this result, we show that the moments can be expanded in the eigenfunction basis, thus opening up the avenue for nonparametric forecasting of the moments. If the collection of probability measures is itself a manifold, we can in addition equip the statistical manifold with the Riemannian metric and use techniques from information geometry. We present applications to ergodic dynamical systems on the 2-torus and the Lorenz 63 system, and show on a real-world example that a small number of eigenvectors is sufficient to reconstruct the moments (here the first four moments) of an atmospheric time series, i.e., the realtime multivariate Madden-Julian oscillation index.
Machine Learning in Python: Principal Component Analysis (PCA) for Handling High-Dimensional Data
Machine Learning in Python: Principal Component Analysis (PCA) for Handling High-Dimensional Data In this video, I will be showing you how to perform principal component analysis (PCA) in Python using the scikit-learn package. PCA represents a powerful learning approach that enables the analysis of high-dimensional data as well as reveal the contribution of descriptors in governing the distribution of data clusters. Particularly, we will be creating PCA scree plot, scores plot and loadings plot. This video is part of the [Python Data Science Project] series. If you're new here, it would mean the world to me if you would consider subscribing to this channel.
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On Quantum Computing and Artificial Intelligence
Mixing quantum computing and Artificial Intelligence (AI) may sound like a new buzzword. However, since quantum computing advances are hinting at profound changes in the very notions of computation, it is natural to reexamine various branches of computer science in the light of these disruptions. As usual, before entering the quantum realm, it is important to get an overview of the classical world. Artificial Intelligence is difficult to define. Probably because intelligence, by itself, is difficult to define.