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A method is presented that allows to reduce a problem described by differential equations with initial and boundary conditions to the problem described only by differential equations. The advantage of using the modified problem for…
We present BAdaCost, a multi-class cost-sensitive classification algorithm. It combines a set of cost-sensitive multi-class weak learners to obtain a strong classification rule within the Boosting framework. To derive the algorithm we…
A significant advance in accelerating neural network training has been the development of normalization methods, permitting the training of deep models both faster and with better accuracy. These advances come with practical challenges: for…
Recent theoretical studies proved that deep neural network (DNN) estimators obtained by minimizing empirical risk with a certain sparsity constraint can attain optimal convergence rates for regression and classification problems. However,…
The explicit regularization and optimality of deep neural networks estimators from independent data have made considerable progress recently. The study of such properties on dependent data is still a challenge. In this paper, we carry out…
Over-parameterized deep neural networks have proven to be able to learn an arbitrary dataset with 100$\%$ training accuracy. Because of a risk of overfitting and computational cost issues, we cannot afford to increase the number of network…
ProBoost, a new boosting algorithm for probabilistic classifiers, is proposed in this work. This algorithm uses the epistemic uncertainty of each training sample to determine the most challenging/uncertain ones; the relevance of these…
State-of-the-art techniques for enhancing robustness of deep networks mostly rely on empirical risk minimization with suitable data augmentation. In this paper, we propose a complementary approach motivated by communication theory, aimed at…
Recent studies have highlighted that deep neural networks (DNNs) are vulnerable to adversarial examples. In this paper, we improve the robustness of DNNs by utilizing techniques of Distance Metric Learning. Specifically, we incorporate…
The empirical loss, commonly referred to as the average loss, is extensively utilized for training machine learning models. However, in order to address the diverse performance requirements of machine learning models, the use of the…
We propose an AdaPtive Noise Augmentation (PANDA) technique to regularize the estimation and construction of undirected graphical models. PANDA iteratively optimizes the objective function given the noise augmented data until convergence to…
Machine Learning facilitates building a large variety of models, starting from elementary linear regression models to very complex neural networks. Neural networks are currently limited by the size of data provided and the huge…
Deep neural networks (DNNs) are powerful learning machines that have enabled breakthroughs in several domains. In this work, we introduce a new retrospective loss to improve the training of deep neural network models by utilizing the prior…
Regularizing continual learning techniques is important for anticipating algorithmic behavior under new realizations of data. We introduce a new approach to continual learning by imposing the properties of a parabolic partial differential…
Multiclass neural network classifiers are typically trained using cross-entropy loss but evaluated using metrics derived from the confusion matrix, such as Accuracy, $F_\beta$-Score, and Matthews Correlation Coefficient. This mismatch…
Ensemble techniques are powerful approaches that combine several weak learners to build a stronger one. As a meta learning framework, ensemble techniques can easily be applied to many machine learning techniques. In this paper we propose a…
In this paper we propose a new family of algorithms, ATENT, for training adversarially robust deep neural networks. We formulate a new loss function that is equipped with an additional entropic regularization. Our loss function considers…
The ability to learn different tasks sequentially is essential to the development of artificial intelligence. In general, neural networks lack this capability, the major obstacle being catastrophic forgetting. It occurs when the…
We design a new adaptive learning algorithm for misclassification cost problems that attempt to reduce the cost of misclassified instances derived from the consequences of various errors. Our algorithm (adaptive cost sensitive learning -…
Several recent works in scientific machine learning have revived interest in the application of neural networks to partial differential equations (PDEs). A popular approach is to aggregate the residual form of the governing PDE and its…