Statistical Learning
Differences Between concat(), merge() and join() with Python
In this article, we will discuss combining the data frames with the help of pandas methods. Sometimes when we are working on a big project and data is coming from different sources then we need to combine those data as one data frame. There are few methods in pandas that data science people are using to make the data frame in more valuable condition. The methods are divided in terms of rows and columns addition. The methods merge() and join() are working based on common keys and indexes with SQL join method approach.
10 Best Data Science with R Online Courses
So you want to learn Data Science with R? Good Decision! Because R programming has various statistical and graphical capabilities. R has a huge variety of libraries to perform statistical analysis. Some most powerful visualization packages in R are ggplot2, ggvis, googleVis, and rCharts. So if you are looking for the Best Online Courses for Data Science with R, then this article will help you.
How to plot XGBoost trees in R - Open Source Automation
In this post, we're going to cover how to plot XGBoost trees in R. XGBoost is a very popular machine learning algorithm, which is frequently used in Kaggle competitions and has many practical use cases. Let's start by loading the packages we'll need. Note that plotting XGBoost trees requires the DiagrammeR package to be installed, so even if you have xgboost installed already, you'll need to make sure you have DiagrammeR also. Next, let's read in our dataset. In this post, we'll be using this customer churn dataset. The label we'll be trying to predict is called "Exited" and is a binary variable with 1 meaning the customer churned (canceled account) vs. 0 meaning the customer did not churn (did not cancel account).
Weighed $\ell_1$ on the simplex: Compressive sensing meets locality
Tasissa, Abiy, Tankala, Pranay, Ba, Demba
Sparse manifold learning algorithms combine techniques in manifold learning and sparse optimization to learn features that could be utilized for downstream tasks. The standard setting of compressive sensing can not be immediately applied to this setup. Due to the intrinsic geometric structure of data, dictionary atoms might be redundant and do not satisfy the restricted isometry property or coherence condition. In addition, manifold learning emphasizes learning local geometry which is not reflected in a standard $\ell_1$ minimization problem. We propose weighted $\ell_0$ and weighted $\ell_1$ metrics that encourage representation via neighborhood atoms suited for dictionary based manifold learning. Assuming that the data is generated from Delaunay triangulation, we show the equivalence of weighted $\ell_1$ and weighted $\ell_0$. We discuss an optimization program that learns the dictionaries and sparse coefficients and demonstrate the utility of our regularization on synthetic and real datasets.
Semi-Supervised Learning of Visual Features by Non-Parametrically Predicting View Assignments with Support Samples
Assran, Mahmoud, Caron, Mathilde, Misra, Ishan, Bojanowski, Piotr, Joulin, Armand, Ballas, Nicolas, Rabbat, Michael
This paper proposes a novel method of learning by predicting view assignments with support samples (PAWS). The method trains a model to minimize a consistency loss, which ensures that different views of the same unlabeled instance are assigned similar pseudo-labels. The pseudo-labels are generated non-parametrically, by comparing the representations of the image views to those of a set of randomly sampled labeled images. The distance between the view representations and labeled representations is used to provide a weighting over class labels, which we interpret as a soft pseudo-label. By non-parametrically incorporating labeled samples in this way, PAWS extends the distance-metric loss used in self-supervised methods such as BYOL and SwAV to the semi-supervised setting. Despite the simplicity of the approach, PAWS outperforms other semi-supervised methods across architectures, setting a new state-of-the-art for a ResNet-50 on ImageNet trained with either 10% or 1% of the labels, reaching 75.5% and 66.5% top-1 respectively. PAWS requires 4x to 12x less training than the previous best methods.
Deep Domain Generalization with Feature-norm Network
Rahman, Mohammad Mahfujur, Fookes, Clinton, Sridharan, Sridha
In this paper, we tackle the problem of training with multiple source domains with the aim to generalize to new domains at test time without an adaptation step. This is known as domain generalization (DG). Previous works on DG assume identical categories or label space across the source domains. In the case of category shift among the source domains, previous methods on DG are vulnerable to negative transfer due to the large mismatch among label spaces, decreasing the target classification accuracy. To tackle the aforementioned problem, we introduce an end-to-end feature-norm network (FNN) which is robust to negative transfer as it does not need to match the feature distribution among the source domains. We also introduce a collaborative feature-norm network (CFNN) to further improve the generalization capability of FNN. The CFNN matches the predictions of the next most likely categories for each training sample which increases each network's posterior entropy. We apply the proposed FNN and CFNN networks to the problem of DG for image classification tasks and demonstrate significant improvement over the state-of-the-art.
Nonlinear Level Set Learning for Function Approximation on Sparse Data with Applications to Parametric Differential Equations
Gruber, Anthony, Gunzburger, Max, Ju, Lili, Teng, Yuankai, Wang, Zhu
A dimension reduction method based on the "Nonlinear Level set Learning" (NLL) approach is presented for the pointwise prediction of functions which have been sparsely sampled. Leveraging geometric information provided by the Implicit Function Theorem, the proposed algorithm effectively reduces the input dimension to the theoretical lower bound with minor accuracy loss, providing a one-dimensional representation of the function which can be used for regression and sensitivity analysis. Experiments and applications are presented which compare this modified NLL with the original NLL and the Active Subspaces (AS) method. While accommodating sparse input data, the proposed algorithm is shown to train quickly and provide a much more accurate and informative reduction than either AS or the original NLL on two example functions with high-dimensional domains, as well as two state-dependent quantities depending on the solutions to parametric differential equations.
Simplified Kalman filter for online rating: one-fits-all approach
Szczecinski, Leszek, Tihon, Raphaëlle
In this work, we deal with the problem of rating in sports, where the skills of the players/teams are inferred from the observed outcomes of the games. Our focus is on the online rating algorithms which estimate the skills after each new game by exploiting the probabilistic models of the relationship between the skills and the game outcome. We propose a Bayesian approach which may be seen as an approximate Kalman filter and which is generic in the sense that it can be used with any skills-outcome model and can be applied in the individual-as well as in the group-sports. We show how the well-know algorithms (such as the Elo, the Glicko, and the TrueSkill algorithms) may be seen as instances of the one-fits-all approach we propose. In order to clarify the conditions under which the gains of the Bayesian approach over the simpler solutions can actually materialize, we critically compare the known and the new algorithms by means of numerical examples using the synthetic as well as the empirical data. In this work we are interested in the rating algorithms that can be systematically derived from the probabilistic models which describe i) how the the skills affect the outcomes of the games, as well as ii) how the skills evolve in time, i.e., characterize the skills dynamics. Using the probabilistic models, the forecasting of the game outcomes is naturally derived from the rating.
Optimal Stopping via Randomized Neural Networks
Herrera, Calypso, Krach, Florian, Ruyssen, Pierre, Teichmann, Josef
This paper presents new machine learning approaches to approximate the solution of optimal stopping problems. The key idea of these methods is to use neural networks, where the hidden layers are generated randomly and only the last layer is trained, in order to approximate the continuation value. Our approaches are applicable for high dimensional problems where the existing approaches become increasingly impractical. In addition, since our approaches can be optimized using a simple linear regression, they are very easy to implement and theoretical guarantees can be provided. In Markovian examples our randomized reinforcement learning approach and in non-Markovian examples our randomized recurrent neural network approach outperform the state-of-the-art and other relevant machine learning approaches.
Risk Bounds for Over-parameterized Maximum Margin Classification on Sub-Gaussian Mixtures
Cao, Yuan, Gu, Quanquan, Belkin, Mikhail
In modern machine learning, complex models such as deep neural networks have received increasing popularity. These complicated models are known to be able to fit noisy training data sets, while at the same time achieving small test errors. In fact, this benign overfitting phenomenon is not a unique feature of deep learning. Even for kernel methods and linear models, Belkin et al. (2018) demonstrated that interpolators on the noisy training data can still perform near optimally on the test data. A series of recent works (Belkin et al., 2019b; Muthukumar et al., 2020b; Hastie et al., 2019; Bartlett et al., 2020) theoretically studied how over-parameterization can achieve small population risk. In particular in Bartlett et al. (2020) the authors considered the setting where the data are generated from a ground-truth linear model with noise, and established a tight population risk bound for the minimum norm linear interpolator with a matching lower bound. More recently, Tsigler and Bartlett (2020) further studied benign overfitting in ridge regression, and established non-asymptotic generalization bounds for over-parametrized ridge regression. They showed that those bounds are tight for a range of regularization parameter values. Notably, these results cover arbitrary covariance structure of the data, and give a nice characterization of how the spectrum of the data covariance matrix affects the population risk in the over-parameterized regime.