Cristian Daniel Alecsa

Cristian Daniel Alecsa

In the present paper we introduce new optimization algorithms for the task of density ratio estimation. More precisely, we consider extending the well-known KMM method using the construction of a suitable loss function, in order to encompass more general situations involving the estimation of density ratio with respect to subsets of the training data and test data, respectively. The associated codes can be found at https://github.com/CDAlecsa/Generalized-KMM.

Cristian Daniel Alecsa

In the present work we propose an unsupervised ensemble method consisting of oblique trees that can address the task of auto-encoding, namely Oblique Forest AutoEncoders (briefly OF-AE). Our method is a natural extension of the eForest encoder introduced in [1]. More precisely, by employing oblique splits consisting in multivariate linear combination of features instead of the axis-parallel ones, we will devise an auto-encoder method through the computation of a sparse solution of a set of linear inequalities consisting of feature values constraints. The code for reproducing our results is available at https://github.com/CDAlecsa/Oblique-Forest-AutoEncoders.

Cristian Daniel Alecsa

It is known that adaptive optimization algorithms represent the key pillar behind the rise of the Machine Learning field. In the Optimization literature numerous studies have been devoted to accelerated gradient methods but only recently adaptive iterative techniques were analyzed from a theoretical point of view. In the present paper we introduce new adaptive algorithms endowed with momentum terms for stochastic non-convex optimization problems. Our purpose is to show a deep connection between accelerated methods endowed with different inertial steps and AMSGrad-type momentum methods. Our methodology is based on the framework of stochastic and possibly non-convex objective mappings, along with some assumptions that are often used in the investigation of adaptive algorithms. In addition to discussing the finite-time horizon analysis in relation to a certain final iteration and the almost sure convergence to stationary points, we shall also look at the worst-case iteration complexity. This will be followed by an estimate for the expectation of the squared Euclidean norm of the gradient. Various computational simulations for the training of neural networks are being used to support the theoretical analysis. For future research we emphasize that there are multiple possible extensions to our work, from which we mention the investigation regarding non-smooth objective functions and the theoretical analysis of a more general formulation that encompass our adaptive optimizers in a stochastic framework.

Cristian Daniel Alecsa, Titus Pinta, Imre Boros

In the following paper we present a new type of optimization algorithms adapted for neural network training. These algorithms are based upon sequential operator splitting technique for some associated dynamical systems. Furthermore, we investigate through numerical simulations the empirical rate of convergence of these iterative schemes toward a local minimum of the loss function, with some suitable choices of the underlying hyper-parameters. We validate the convergence of these optimizers using the results of the accuracy and of the loss function on the MNIST, MNIST-Fashion and CIFAR 10 classification datasets.