In this paper, we introduce a new learning strategy based on a seminal idea of Mojirsheibani (1999, 2000, 2002a, 2002b), who proposed a smart method for combining several classifiers, relying on a consensus notion. In many aggregation methods, the prediction for a new observation x is computed by building a linear or convex combination over a collection of basic estimators r1(x),. .. , rm(x) previously calibrated using a training data set. Mojirsheibani proposes to compute the prediction associated to a new observation by combining selected outputs of the training examples. The output of a training example is selected if some kind of consensus is observed: the predictions computed for the training example with the different machines have to be "similar" to the prediction for the new observation. This approach has been recently extended to the context of regression in Biau et al. (2016). In the original scheme, the agreement condition is actually required to hold for all individual estimators, which appears inadequate if there is one bad initial estimator. In practice, a few disagreements are allowed ; for establishing the theoretical results, the proportion of estimators satisfying the condition is required to tend to 1. In this paper, we propose an alternative procedure, mixing the previous consensus ideas on the predictions with the Euclidean distance computed between entries. This may be seen as an alternative approach allowing to reduce the effect of a possibly bad estimator in the initial list, using a constraint on the inputs. We prove the consistency of our strategy in classification and in regression. We also provide some numerical experiments on simulated and real data to illustrate the benefits of this new aggregation method. On the whole, our practical study shows that our method may perform much better than the original combination technique, and, in particular, exhibit far less variance. We also show on simulated examples that this procedure mixing inputs and outputs is still robust to high dimensional inputs.

A few weeks ago I started seriously studying Machine Learning (ML). I have taken some courses and read some books before, but now I am taking a step ahead. I do plan to start working on ML projects and really get into the field. To me, the only way to make sure you understand something, is the fact that you are able to explain it to others. Because of this, I decided to write a Machine Learning 101 blog post, in which I explain some (very) basic ML concepts.

The goal in extreme multi-label classification is to learn a classifier which can assign a small subset of relevant labels to an instance from an extremely large set of target labels. Datasets in extreme classification exhibit a long tail of labels which have small number of positive training instances. In this work, we pose the learning task in extreme classification with large number of tail-labels as learning in the presence of adversarial perturbations. This view motivates a robust optimization framework and equivalence to a corresponding regularized objective. Under the proposed robustness framework, we demonstrate efficacy of Hamming loss for tail-label detection in extreme classification. The equivalent regularized objective, in combination with proximal gradient based optimization, performs better than state-of-the-art methods on propensity scored versions of precision@k and nDCG@k(upto 20% relative improvement over PFastreXML - a leading tree-based approach and 60% relative improvement over SLEEC - a leading label-embedding approach). Furthermore, we also highlight the sub-optimality of a sparse solver in a widely used package for large-scale linear classification, which is interesting in its own right. We also investigate the spectral properties of label graphs for providing novel insights towards understanding the conditions governing the performance of Hamming loss based one-vs-rest scheme vis-\`a-vis label embedding methods.

Methods that learn representations of nodes in a graph play a critical role in network analysis since they enable many downstream learning tasks. We propose Graph2Gauss - an approach that can efficiently learn versatile node embeddings on large scale (attributed) graphs that show strong performance on tasks such as link prediction and node classification. Unlike most approaches that represent nodes as point vectors in a low-dimensional continuous space, we embed each node as a Gaussian distribution, allowing us to capture uncertainty about the representation. Furthermore, we propose an unsupervised method that handles inductive learning scenarios and is applicable to different types of graphs: plain/attributed, directed/undirected. By leveraging both the network structure and the associated node attributes, we are able to generalize to unseen nodes without additional training. To learn the embeddings we adopt a personalized ranking formulation w.r.t. the node distances that exploits the natural ordering of the nodes imposed by the network structure. Experiments on real world networks demonstrate the high performance of our approach, outperforming state-of-the-art network embedding methods on several different tasks. Additionally, we demonstrate the benefits of modeling uncertainty - by analyzing it we can estimate neighborhood diversity and detect the intrinsic latent dimensionality of a graph.

Graph Convolutional Networks (GCNs) have shown significant improvements in semi-supervised learning on graph-structured data. Concurrently, unsupervised learning of graph embeddings has benefited from the information contained in random walks. In this paper, we propose a model: Network of GCNs (N-GCN), which marries these two lines of work. At its core, N-GCN trains multiple instances of GCNs over node pairs discovered at different distances in random walks, and learns a combination of the instance outputs which optimizes the classification objective. Our experiments show that our proposed N-GCN model improves state-of-the-art baselines on all of the challenging node classification tasks we consider: Cora, Citeseer, Pubmed, and PPI. In addition, our proposed method has other desirable properties, including generalization to recently proposed semi-supervised learning methods such as GraphSAGE, allowing us to propose N-SAGE, and resilience to adversarial input perturbations.

As we discussed in the first article, linear regression is a supervised learning algorithm where the output is continuous valued. Think of r t as the output and X t as the training examples. This is the ideal scenario that we would like to have: A function that predicts the output perfectly from the training examples. But this does not generally happen in the real world. There is an additional noise that needs to be added to the function to get the required output.

Vote-boosting is a sequential ensemble learning method in which the individual classifiers are built on different weighted versions of the training data. To build a new classifier, the weight of each training instance is determined in terms of the degree of disagreement among the current ensemble predictions for that instance. For low class-label noise levels, especially when simple base learners are used, emphasis should be made on instances for which the disagreement rate is high. When more flexible classifiers are used and as the noise level increases, the emphasis on these uncertain instances should be reduced. In fact, at sufficiently high levels of class-label noise, the focus should be on instances on which the ensemble classifiers agree. The optimal type of emphasis can be automatically determined using cross-validation. An extensive empirical analysis using the beta distribution as emphasis function illustrates that vote-boosting is an effective method to generate ensembles that are both accurate and robust.

Artificial Intelligence is a branch of Computer Science ( or Science) which deals with the creation of intelligent systems. Intelligent systems are those systems which posses intelligence just like humans. The science of Artificial intelligence is not new, The term Artificial intelligence has been mentioned in manuscripts of Ancient Greece and Egypt. Greeks believed in god Hephaestus, also known as God of Blacksmiths, according to a Greek mythology Hephaestus made intelligent weapons for all Gods, in their view, the goal of Artificial intelligence is to: be helpful for people to achieve a certain goal, be able to operate automatically and be programmed in advance to react in different ways depending on the situation. Well, The term Artificial Intelligence has become popular in the field of Entertainment, we can see lots of movies based on the concept of Super intelligence.

Without access to large compute clusters, building random forests on large datasets is still a challenging problem. This is, in particular, the case if fully-grown trees are desired. We propose a simple yet effective framework that allows to efficiently construct ensembles of huge trees for hundreds of millions or even billions of training instances using a cheap desktop computer with commodity hardware. The basic idea is to consider a multi-level construction scheme, which builds top trees for small random subsets of the available data and which subsequently distributes all training instances to the top trees' leaves for further processing. While being conceptually simple, the overall efficiency crucially depends on the particular implementation of the different phases. The practical merits of our approach are demonstrated using dense datasets with hundreds of millions of training instances.

The study of ML algorithms has gained immense traction post the Harvard Business Review article terming a'Data Scientist' as the'Sexiest job of the 21st century'. So, for those starting out in the field of ML, we decided to do a reboot of our immensely popular Gold blog The 10 Algorithms Machine Learning Engineers need to know - albeit this post is targetted towards beginners. ML algorithms are those that can learn from data and improve from experience, without human intervention. Learning tasks may include learning the function that maps the input to the output, learning the hidden structure in unlabeled data; or'instance-based learning', where a class label is produced for a new instance by comparing the new instance (row) to instances from the training data, which were stored in memory. 'Instance-based learning' does not create an abstraction from specific instances. Supervised learning can be explained as follows: use labeled training data to learn the mapping function from the input variables (X) to the output variable (Y).