This part of the gradient behaves similarly for permuted and unpermuted examples. In Eq. 25 we see that the contribution to the label dependent part of the gradient from permuted examples vanishes for large datasets, while the contribution from unpermuted examples does not provided the cross correlation between input features and labels is nonzero. This suggests that with small weight initialization, the gradient descent dynamics initially ignores the labels of permuted examples. Figure A.1 shows a breakdown of how the two components of the gradient computed on both unpermuted and permuted examples evolve over the course of training for the different layers of the VGG16 model trained on CIFAR-100. We see that the label dependent part behaves qualitatively differently for the unpermuted examples than for the permuted examples, as the permuted examples give close to zero contribution early in training in agreement with Eq. 25. The label independent part of the gradient shows similar trends between unpermuted and permuted examples, though in the final epochs, the unpermuted examples have a slightly larger label independent gradient indicating slightly greater model confidence on these examples. As the label dependent and label independent parts of the gradient have differing signs, they compete with each other and cancel when the loss is minimized, but are not independently zero and in fact grow during training. The slightly larger label independent gradient for unpermuted examples is balanced by a corresponding slightly larger label dependent gradient at the end of training.

The NIFTY 50 index is National Stock Exchange of India's benchmark broad based stock market index for the Indian equity market. Full form of NIFTY is National Stock Exchange Fifty. It represents the weighted average of 50 Indian company stocks in 12 sectors and is one of the two main stock indices used in India, the other being the BSE Sensex. In this blog, we will see how we can use the various Time Series algorithms to predict how the NIFTY50 index will move over the next 30 days. To download the data, we can go to the Yahoo Finance site and download the historical data for the NIFTY50 index.

Machine learning is a field of computer science that uses statistical techniques to give computer programs the ability to learn from past experiences and improve how they perform specific tasks. In this step-by-step tutorial, you'll cover the basics of setting up a Python numerical computation environment for machine learning on a Windows machine using the Anaconda Python distribution. In this course on face detection with Python, you'll learn about a historically important algorithm for object detection that can be successfully applied to finding the location of a human face within an image. In this introductory tutorial, you'll learn how to simply segment an object from an image based on color in Python using OpenCV. A popular computer vision library written in C/C with bindings for Python, OpenCV provides easy ways of manipulating color spaces.

With the advent of Artificial Intelligence (AI)-empowered communications, industry, academia, and standardization organizations are progressing on the definition of mechanisms and procedures to address the increasing complexity of future 5G and beyond communications. In this context, the International Telecommunication Union (ITU) organized the first AI for 5G Challenge to bring industry and academia together to introduce and solve representative problems related to the application of Machine Learning (ML) to networks. In this paper, we present the results gathered from Problem Statement~13 (PS-013), organized by Universitat Pompeu Fabra (UPF), which primary goal was predicting the performance of next-generation Wireless Local Area Networks (WLANs) applying Channel Bonding (CB) techniques. In particular, we overview the ML models proposed by participants (including Artificial Neural Networks, Graph Neural Networks, Random Forest regression, and gradient boosting) and analyze their performance on an open dataset generated using the IEEE 802.11ax-oriented Komondor network simulator. The accuracy achieved by the proposed methods demonstrates the suitability of ML for predicting the performance of WLANs. Moreover, we discuss the importance of abstracting WLAN interactions to achieve better results, and we argue that there is certainly room for improvement in throughput prediction through ML.

In this work, we study the transfer learning problem under high-dimensional generalized linear models (GLMs), which aim to improve the fit on target data by borrowing information from useful source data. Given which sources to transfer, we propose an oracle algorithm and derive its $\ell_2$-estimation error bounds. The theoretical analysis shows that under certain conditions, when the target and source are sufficiently close to each other, the estimation error bound could be improved over that of the classical penalized estimator using only target data. When we don't know which sources to transfer, an algorithm-free transferable source detection approach is introduced to detect informative sources. The detection consistency is proved under the high-dimensional GLM transfer learning setting. Extensive simulations and a real-data experiment verify the effectiveness of our algorithms.

Binary classification, in the first place, deals with decision tools (classifiers) that facilitate the prediction of the classes of instances on the basis of the so-called features of the instances. Accordingly, the simplest classifiers are crisp (or discrete) in the sense of having the set {0, 1} as output range: 1 for'predict positive class', 0 for'predict negative class. Scoring (or soft) classifiers provide output in a continuous range, usually with the interpretation that high values indicate high likelihood of the instance belonging to the positive class, while low values suggest that membership of the negative class is more likely. In many applications of classification, there is a need for'calibrated' probabilistic classifiers which reflect the likelihood of the positive class given the features of an instance in a frequentist statistical sense (Platt, 2000; Zadrozny and Elkan, 2002; Cohen and Goldszmidt, 2004; Kull et al., 2017). How to best achieve good calibration and how to measure it are active research areas (Böken, 2021; Roelofs et al., 2020).

We posit a new mechanism for cooperation in multi-agent reinforcement learning (MARL) based upon any nonlinear function of the team's long-term state-action occupancy measure, i.e., a \emph{general utility}. This subsumes the cumulative return but also allows one to incorporate risk-sensitivity, exploration, and priors. % We derive the {\bf D}ecentralized {\bf S}hadow Reward {\bf A}ctor-{\bf C}ritic (DSAC) in which agents alternate between policy evaluation (critic), weighted averaging with neighbors (information mixing), and local gradient updates for their policy parameters (actor). DSAC augments the classic critic step by requiring agents to (i) estimate their local occupancy measure in order to (ii) estimate the derivative of the local utility with respect to their occupancy measure, i.e., the "shadow reward". DSAC converges to $\epsilon$-stationarity in $\mathcal{O}(1/\epsilon^{2.5})$ (Theorem \ref{theorem:final}) or faster $\mathcal{O}(1/\epsilon^{2})$ (Corollary \ref{corollary:communication}) steps with high probability, depending on the amount of communications. We further establish the non-existence of spurious stationary points for this problem, that is, DSAC finds the globally optimal policy (Corollary \ref{corollary:global}). Experiments demonstrate the merits of goals beyond the cumulative return in cooperative MARL.

Finding parameters in a deep neural network (NN) that fit training data is a nonconvex optimization problem, but a basic first-order optimization method (gradient descent) finds a global optimizer with perfect fit (zero-loss) in many practical situations. We examine this phenomenon for the case of Residual Neural Networks (ResNet) with smooth activation functions in a limiting regime in which both the number of layers (depth) and the number of neurons in each layer (width) go to infinity. First, we use a mean-field-limit argument to prove that the gradient descent for parameter training becomes a gradient flow for a probability distribution that is characterized by a partial differential equation (PDE) in the large-NN limit. Next, we show that the solution to the PDE converges in the training time to a zero-loss solution. Together, these results imply that the training of the ResNet gives a near-zero loss if the ResNet is large enough. We give estimates of the depth and width needed to reduce the loss below a given threshold, with high probability.

Graphon is a nonparametric model that generates graphs with arbitrary sizes and can be induced from graphs easily. Based on this model, we propose a novel algorithmic framework called \textit{graphon autoencoder} to build an interpretable and scalable graph generative model. This framework treats observed graphs as induced graphons in functional space and derives their latent representations by an encoder that aggregates Chebshev graphon filters. A linear graphon factorization model works as a decoder, leveraging the latent representations to reconstruct the induced graphons (and the corresponding observed graphs). We develop an efficient learning algorithm to learn the encoder and the decoder, minimizing the Wasserstein distance between the model and data distributions. This algorithm takes the KL divergence of the graph distributions conditioned on different graphons as the underlying distance and leads to a reward-augmented maximum likelihood estimation. The graphon autoencoder provides a new paradigm to represent and generate graphs, which has good generalizability and transferability.

Ensemble learning refers to machine learning models that combine the predictions from two or more models. Ensembles are an advanced approach to machine learning that are often used when the capability and skill of the predictions are more important than using a simple and understandable model. As such, they are often used by top and winning participants in machine learning competitions like the One Million Dollar Netflix Prize and Kaggle Competitions. Modern machine learning libraries like scikit-learn Python provide a suite of advanced ensemble learning methods that are easy to configure and use correctly without data leakage, a common concern when using ensemble algorithms. In this crash course, you will discover how you can get started and confidently bring ensemble learning algorithms to your predictive modeling project with Python in seven days. This is a big and important post.