It was recently shown that architectural, regularization and rehearsal strategies can be used to train deep models sequentially on a number of disjoint tasks without forgetting previously acquired knowledge. However, these strategies are still unsatisfactory if the tasks are not disjoint but constitute a single incremental task (e.g., class-incremental learning). In this paper we point out the differences between multi-task and single-incremental-task scenarios and show that well-known approaches such as LWF, EWC and SI are not ideal for incremental task scenarios. A new approach, denoted as AR1, combining architectural and regularization strategies is then specifically proposed. AR1 overhead (in term of memory and computation) is very small thus making it suitable for online learning. When tested on CORe50 and iCIFAR-100, AR1 outperformed existing regularization strategies by a good margin.

In this study, we predict the outcome of the football matches in the FIFA World Cup 2018 to be held in Russia this summer. We do this using classification models over a dataset of historic football results that includes attributes from the playing teams by rating them in attack, midfield, defence, aggression, pressure, chance creation and building ability. This last training data was a result of merging international matches results with AE games ratings of the teams considering the timeline of the matches with their respective statistics. Final predictions show the four countries with the most chances of getting to the semifinals as France, Brazil, Spain and Germany while giving Spain as the winner. The objective of this study is to build a predictive model that will allow us to make good predictions for the coming World Cup 2018 so we looked for dataset with historic data for match results, for this purpose we chose a dataset from Kaggle with data of almost 40,000 international matches played between 1872 and 2018.

By building up on the recent theory that established the connection between implicit generative modeling and optimal transport, in this study, we propose a novel parameter-free algorithm for learning the underlying distributions of complicated datasets and sampling from them. The proposed algorithm is based on a functional optimization problem, which aims at finding a measure that is close to the data distribution as much as possible and also expressive enough for generative modeling purposes. We formulate the problem as a gradient flow in the space of probability measures. The connections between gradient flows and stochastic differential equations let us develop a computationally efficient algorithm for solving the optimization problem, where the resulting algorithm resembles the recent dynamics-based Markov Chain Monte Carlo algorithms. We provide formal theoretical analysis where we prove finite-time error guarantees for the proposed algorithm. Our experimental results support our theory and shows that our algorithm is able to capture the structure of challenging distributions.

The PARAFAC2 is a multimodal factor analysis model suitable for analyzing multi-way data when one of the modes has incomparable observation units, for example because of differences in signal sampling or batch sizes. A fully probabilistic treatment of the PARAFAC2 is desirable in order to improve robustness to noise and provide a well founded principle for determining the number of factors, but challenging because the factor loadings are constrained to be orthogonal. We develop two probabilistic formulations of the PARAFAC2 along with variational procedures for inference: In the one approach, the mean values of the factor loadings are orthogonal leading to closed form variational updates, and in the other, the factor loadings themselves are orthogonal using a matrix Von Mises-Fisher distribution. We contrast our probabilistic formulation to the conventional direct fitting algorithm based on maximum likelihood. On simulated data and real fluorescence spectroscopy and gas chromatography-mass spectrometry data, we compare our approach to the conventional PARAFAC2 model estimation and find that the probabilistic formulation is more robust to noise and model order misspecification. The probabilistic PARAFAC2 thus forms a promising framework for modeling multi-way data accounting for uncertainty.

Graph Weighted Models (GWMs) have recently been proposed as a natural generalization of weighted automata over strings and trees to arbitrary families of labeled graphs (and hypergraphs). A GWM generically associates a labeled graph with a tensor network and computes a value by successive contractions directed by its edges. In this paper, we consider the problem of learning GWMs defined over the graph family of pictures (or 2-dimensional words). As a proof of concept, we consider regression and classification tasks over the simple Bars & Stripes and Shifting Bits picture languages and provide an experimental study investigating whether these languages can be learned in the form of a GWM from positive and negative examples using gradient-based methods. Our results suggest that this is indeed possible and that investigating the use of gradient-based methods to learn picture series and functions computed by GWMs over other families of graphs could be a fruitful direction.

Several representation learning and, more broadly, dimensionality reduction techniques seek to produce representations of the data that are orthogonal (uncorrelated). Examples include PCA, CCA, Kernel/Deep CCA, the ACE algorithm and correspondence analysis (CA). For a fixed data distribution, all finite variance representations belong to the same function space regardless of how they are derived. In this work, we present a theoretical framework for analyzing this function space, and demonstrate how a basis for this space can be found using neural networks. We show that this framework (i) underlies recent multi-view representation learning methods, (ii) enables classical exploratory statistical techniques such as CA to be scaled via neural networks, and (iii) can be used to derive new methods for comparing black-box models. We illustrate these applications empirically through different datasets.

Well-known for its simplicity and effectiveness in classification, AdaBoost, however, suffers from overfitting when class-conditional distributions have significant overlap. Moreover, it is very sensitive to noise that appears in the labels. This article tackles the above limitations simultaneously via optimizing a modified loss function (i.e., the conditional risk). The proposed approach has the following two advantages. (1) It is able to directly take into account label uncertainty with an associated label confidence. (2) It introduces a "trustworthiness" measure on training samples via the Bayesian risk rule, and hence the resulting classifier tends to have finite sample performance that is superior to that of the original AdaBoost when there is a large overlap between class conditional distributions. Theoretical properties of the proposed method are investigated. Extensive experimental results using synthetic data and real-world data sets from UCI machine learning repository are provided. The empirical study shows the high competitiveness of the proposed method in predication accuracy and robustness when compared with the original AdaBoost and several existing robust AdaBoost algorithms.

Conventional embedding methods directly associate each symbol with a continuous embedding vector, which is equivalent to applying a linear transformation based on a "one-hot" encoding of the discrete symbols. Despite its simplicity, such approach yields the number of parameters that grows linearly with the vocabulary size and can lead to overfitting. In this work, we propose a much more compact K-way D-dimensional discrete encoding scheme to replace the "one-hot" encoding. In the proposed "KD encoding", each symbol is represented by a $D$-dimensional code with a cardinality of $K$, and the final symbol embedding vector is generated by composing the code embedding vectors. To end-to-end learn semantically meaningful codes, we derive a relaxed discrete optimization approach based on stochastic gradient descent, which can be generally applied to any differentiable computational graph with an embedding layer. In our experiments with various applications from natural language processing to graph convolutional networks, the total size of the embedding layer can be reduced up to 98\% while achieving similar or better performance.

One of the most popular applications of machine learning in marketing is cluster analysis. Letting the model group website visitors or customers into clusters reveals potential segmentation methods that might not have come to mind otherwise. Webmasters can tailor communications and promotions based on the common interests of a segment, and lead generation managers can do the same with in their lead conversion and nurturing strategies. This example shows how you can first analyze your website visitors using the traditional BI approach of segmenting users by which section of the website the visited, the search keyword they entered via, and the time spent on the site. Then with machine learning you can see how four clusters were found just by providing the model with the raw data and no preconceived notions of segmentation.

In the previous blog posts in this series, we discussed the motivation for clustering attacks and the data used and how to calculate the distance between two attacks using different methods on each feature we extracted. In this final blog post, we'll discuss the clustering algorithm itself – how to use the distance we calculated to create clusters from the data. We will discuss clustering in real time when only a small amount of data can be stored in memory. Finally, we'll show some results of the algorithm based on real data from Imperva customers. Now we have all the basic ingredients to input into the algorithm.