Newton Method-based Subspace Support Vector Data Description

In this paper, we present an adaptation of Newton's method for the optimization of Subspace Support Vector Data Description (S-SVDD). The objective of S-SVDD is to map the original data to a subspace optimized for one-class classification, and the iterative optimization process of data mapping and description in S-SVDD relies on gradient descent. However, gradient descent only utilizes first-order information, which may lead to suboptimal results. To address this limitation, we leverage Newton's method to enhance data mapping and data description for an improved optimization of subspace learning-based one-class classification. By incorporating this auxiliary information, Newton's method offers a more efficient strategy for subspace learning in one-class classification as compared to gradient-based optimization. The paper discusses the limitations of gradient descent and the advantages of using Newton's method in subspace learning for one-class classification tasks. We provide both linear and nonlinear formulations of Newton's method-based optimization for S-SVDD. In our experiments, we explored both the minimization and maximization strategies of the objective. The results demonstrate that the proposed optimization strategy outperforms the gradient-based S-SVDD in most cases.Comment: 8 pages, 2 figures, 2 tables, 1 Algorithm. Accepted at IEEE Symposium Series on Computational Intelligence 202

Color Constancy Convolutional Autoencoder

In this paper, we study the importance of pre-training for the generalization capability in the color constancy problem. We propose two novel approaches based on convolutional autoencoders: an unsupervised pre-training algorithm using a fine-tuned encoder and a semi-supervised pre-training algorithm using a novel composite-loss function. This enables us to solve the data scarcity problem and achieve competitive, to the state-of-the-art, results while requiring much fewer parameters on ColorChecker RECommended dataset. We further study the over-fitting phenomenon on the recently introduced version of INTEL-TUT Dataset for Camera Invariant Color Constancy Research, which has both field and non-field scenes acquired by three different camera models.Comment: 6 pages, 1 figure, 3 table

Class-wise Generalization Error: an Information-Theoretic Analysis

Existing generalization theories of supervised learning typically take a holistic approach and provide bounds for the expected generalization over the whole data distribution, which implicitly assumes that the model generalizes similarly for all the classes. In practice, however, there are significant variations in generalization performance among different classes, which cannot be captured by the existing generalization bounds. In this work, we tackle this problem by theoretically studying the class-generalization error, which quantifies the generalization performance of each individual class. We derive a novel information-theoretic bound for class-generalization error using the KL divergence, and we further obtain several tighter bounds using the conditional mutual information (CMI), which are significantly easier to estimate in practice. We empirically validate our proposed bounds in different neural networks and show that they accurately capture the complex class-generalization error behavior. Moreover, we show that the theoretical tools developed in this paper can be applied in several applications beyond this context.Comment: 26 page

On Feature Diversity in Energy-based Models

Energy-based learning is a powerful learning paradigm that encapsulates various discriminative and generative approaches. An energy-based model (EBM) is typically formed of inner-model(s) that learn a combination of the different features to generate an energy mapping for each input configuration. In this paper, we focus on the diversity of the produced feature set. We extend the probably approximately correct (PAC) theory of EBMs and analyze the effect of redundancy reduction on the performance of EBMs. We derive generalization bounds for various learning contexts, i.e., regression, classification, and implicit regression, with different energy functions and we show that indeed reducing redundancy of the feature set can consistently decrease the gap between the true and empirical expectation of the energy and boosts the performance of the model.Comment: 18 pages, 3 figure

Reducing Redundancy in the Bottleneck Representation of the Autoencoders

Autoencoders are a type of unsupervised neural networks, which can be used to solve various tasks, e.g., dimensionality reduction, image compression, and image denoising. An AE has two goals: (i) compress the original input to a low-dimensional space at the bottleneck of the network topology using an encoder, (ii) reconstruct the input from the representation at the bottleneck using a decoder. Both encoder and decoder are optimized jointly by minimizing a distortion-based loss which implicitly forces the model to keep only those variations of input data that are required to reconstruct the and to reduce redundancies. In this paper, we propose a scheme to explicitly penalize feature redundancies in the bottleneck representation. To this end, we propose an additional loss term, based on the pair-wise correlation of the neurons, which complements the standard reconstruction loss forcing the encoder to learn a more diverse and richer representation of the input. We tested our approach across different tasks: dimensionality reduction using three different dataset, image compression using the MNIST dataset, and image denoising using fashion MNIST. The experimental results show that the proposed loss leads consistently to superior performance compared to the standard AE loss.Comment: 6 pages,4 figures. The paper is under consideration at Pattern Recognition Letter

Within-layer Diversity Reduces Generalization Gap

Neural networks are composed of multiple layers arranged in a hierarchical structure jointly trained with a gradient-based optimization, where the errors are back-propagated from the last layer back to the first one. At each optimization step, neurons at a given layer receive feedback from neurons belonging to higher layers of the hierarchy. In this paper, we propose to complement this traditional 'between-layer' feedback with additional 'within-layer' feedback to encourage diversity of the activations within the same layer. To this end, we measure the pairwise similarity between the outputs of the neurons and use it to model the layer's overall diversity. By penalizing similarities and promoting diversity, we encourage each neuron to learn a distinctive representation and, thus, to enrich the data representation learned within the layer and to increase the total capacity of the model. We theoretically study how the within-layer activation diversity affects the generalization performance of a neural network and prove that increasing the diversity of hidden activations reduces the estimation error. In addition to the theoretical guarantees, we present an empirical study on three datasets confirming that the proposed approach enhances the performance of state-of-the-art neural network models and decreases the generalization gap.Comment: 18 pages, 1 figure, 3 Table

Efficient CNN with uncorrelated Bag of Features pooling

Despite the superior performance of CNN, deploying them on low computational power devices is still limited as they are typically computationally expensive. One key cause of the high complexity is the connection between the convolution layers and the fully connected layers, which typically requires a high number of parameters. To alleviate this issue, Bag of Features (BoF) pooling has been recently proposed. BoF learns a dictionary, that is used to compile a histogram representation of the input. In this paper, we propose an approach that builds on top of BoF pooling to boost its efficiency by ensuring that the items of the learned dictionary are non-redundant. We propose an additional loss term, based on the pair-wise correlation of the items of the dictionary, which complements the standard loss to explicitly regularize the model to learn a more diverse and rich dictionary. The proposed strategy yields an efficient variant of BoF and further boosts its performance, without any additional parameters.Comment: 6 pages, 2 Figure

Graph Embedding with Data Uncertainty

spectral-based subspace learning is a common data preprocessing step in many machine learning pipelines. The main aim is to learn a meaningful low dimensional embedding of the data. However, most subspace learning methods do not take into consideration possible measurement inaccuracies or artifacts that can lead to data with high uncertainty. Thus, learning directly from raw data can be misleading and can negatively impact the accuracy. In this paper, we propose to model artifacts in training data using probability distributions; each data point is represented by a Gaussian distribution centered at the original data point and having a variance modeling its uncertainty. We reformulate the Graph Embedding framework to make it suitable for learning from distributions and we study as special cases the Linear Discriminant Analysis and the Marginal Fisher Analysis techniques. Furthermore, we propose two schemes for modeling data uncertainty based on pair-wise distances in an unsupervised and a supervised contexts.Comment: 20 pages, 4 figure

Monte Carlo Dropout Ensembles for Robust Illumination Estimation

Computational color constancy is a preprocessing step used in many camera systems. The main aim is to discount the effect of the illumination on the colors in the scene and restore the original colors of the objects. Recently, several deep learning-based approaches have been proposed to solve this problem and they often led to state-of-the-art performance in terms of average errors. However, for extreme samples, these methods fail and lead to high errors. In this paper, we address this limitation by proposing to aggregate different deep learning methods according to their output uncertainty. We estimate the relative uncertainty of each approach using Monte Carlo dropout and the final illumination estimate is obtained as the sum of the different model estimates weighted by the log-inverse of their corresponding uncertainties. The proposed framework leads to state-of-the-art performance on INTEL-TAU dataset.Comment: 7 pages,6 figure