Implicit Bayes Adaptation: A Collaborative Transport Approach

The power and flexibility of Optimal Transport (OT) have pervaded a wide spectrum of problems, including recent Machine Learning challenges such as unsupervised domain adaptation. Its essence of quantitatively relating two probability distributions by some optimal metric, has been creatively exploited and shown to hold promise for many real-world data challenges. In a related theme in the present work, we posit that domain adaptation robustness is rooted in the intrinsic (latent) representations of the respective data, which are inherently lying in a non-linear submanifold embedded in a higher dimensional Euclidean space. We account for the geometric properties by refining the $l^2$ Euclidean metric to better reflect the geodesic distance between two distinct representations. We integrate a metric correction term as well as a prior cluster structure in the source data of the OT-driven adaptation. We show that this is tantamount to an implicit Bayesian framework, which we demonstrate to be viable for a more robust and better-performing approach to domain adaptation. Substantiating experiments are also included for validation purposes.

Fast OT for Latent Domain Adaptation

In this paper, we address the problem of unsupervised Domain Adaptation. The need for such an adaptation arises when the distribution of the target data differs from that which is used to develop the model and the ground truth information of the target data is unknown. We propose an algorithm that uses optimal transport theory with a verifiably efficient and implementable solution to learn the best latent feature representation. This is achieved by minimizing the cost of transporting the samples from the target domain to the distribution of the source domain.

Information Fusion: Scaling Subspace-Driven Approaches

In this work, we seek to exploit the deep structure of multi-modal data to robustly exploit the group subspace distribution of the information using the Convolutional Neural Network (CNN) formalism. Upon unfolding the set of subspaces constituting each data modality, and learning their corresponding encoders, an optimized integration of the generated inherent information is carried out to yield a characterization of various classes. Referred to as deep Multimodal Robust Group Subspace Clustering (DRoGSuRe), this approach is compared against the independently developed state-of-the-art approach named Deep Multimodal Subspace Clustering (DMSC). Experiments on different multimodal datasets show that our approach is competitive and more robust in the presence of noise.

Refining Self-Supervised Learning in Imaging: Beyond Linear Metric

We introduce in this paper a new statistical perspective, exploiting the Jaccard similarity metric, as a measure-based metric to effectively invoke non-linear features in the loss of self-supervised contrastive learning. Specifically, our proposed metric may be interpreted as a dependence measure between two adapted projections learned from the so-called latent representations. This is in contrast to the cosine similarity measure in the conventional contrastive learning model, which accounts for correlation information. To the best of our knowledge, this effectively non-linearly fused information embedded in the Jaccard similarity, is novel to self-supervision learning with promising results. The proposed approach is compared to two state-of-the-art self-supervised contrastive learning methods on three image datasets. We not only demonstrate its amenable applicability in current ML problems, but also its improved performance and training efficiency.

Deep Transform and Metric Learning Networks

Based on its great successes in inference and denosing tasks, Dictionary Learning (DL) and its related sparse optimization formulations have garnered a lot of research interest. While most solutions have focused on single layer dictionaries, the recently improved Deep DL methods have also fallen short on a number of issues. We hence propose a novel Deep DL approach where each DL layer can be formulated and solved as a combination of one linear layer and a Recurrent Neural Network, where the RNN is flexibly regraded as a layer-associated learned metric. Our proposed work unveils new insights between the Neural Networks and Deep DL, and provides a novel, efficient and competitive approach to jointly learn the deep transforms and metrics. Extensive experiments are carried out to demonstrate that the proposed method can not only outperform existing Deep DL, but also state-of-the-art generic Convolutional Neural Networks.

Latent Code-Based Fusion: A Volterra Neural Network Approach

We propose a deep structure encoder using the recently introduced Volterra Neural Networks (VNNs) to seek a latent representation of multi-modal data whose features are jointly captured by a union of subspaces. The so-called self-representation embedding of the latent codes leads to a simplified fusion which is driven by a similarly constructed decoding. The Volterra Filter architecture achieved reduction in parameter complexity is primarily due to controlled non-linearities being introduced by the higher-order convolutions in contrast to generalized activation functions. Experimental results on two different datasets have shown a significant improvement in the clustering performance for VNNs auto-encoder over conventional Convolutional Neural Networks (CNNs) auto-encoder. In addition, we also show that the proposed approach demonstrates a much-improved sample complexity over CNN-based auto-encoder with a superb robust classification performance.

Robust Group Subspace Recovery: A New Approach for Multi-Modality Data Fusion

Robust Subspace Recovery (RoSuRe) algorithm was recently introduced as a principled and numerically efficient algorithm that unfolds underlying Unions of Subspaces (UoS) structure, present in the data. The union of Subspaces (UoS) is capable of identifying more complex trends in data sets than simple linear models. We build on and extend RoSuRe to prospect the structure of different data modalities individually. We propose a novel multi-modal data fusion approach based on group sparsity which we refer to as Robust Group Subspace Recovery (RoGSuRe). Relying on a bi-sparsity pursuit paradigm and non-smooth optimization techniques, the introduced framework learns a new joint representation of the time series from different data modalities, respecting an underlying UoS model. We subsequently integrate the obtained structures to form a unified subspace structure. The proposed approach exploits the structural dependencies between the different modalities data to cluster the associated target objects. The resulting fusion of the unlabeled sensors' data from experiments on audio and magnetic data has shown that our method is competitive with other state of the art subspace clustering methods. The resulting UoS structure is employed to classify newly observed data points, highlighting the abstraction capacity of the proposed method.

Deep Transform and Metric Learning Network: Wedding Deep Dictionary Learning and Neural Networks

On account of its many successes in inference tasks and denoising applications, Dictionary Learning (DL) and its related sparse optimization problems have garnered a lot of research interest. While most solutions have focused on single layer dictionaries, the improved recently proposed Deep DL (DDL) methods have also fallen short on a number of issues. We propose herein, a novel DDL approach where each DL layer can be formulated as a combination of one linear layer and a Recurrent Neural Network (RNN). The RNN is shown to flexibly account for the layer-associated and learned metric. Our proposed work unveils new insights into Neural Networks and DDL and provides a new, efficient and competitive approach to jointly learn a deep transform and a metric for inference applications. Extensive experiments are carried out to demonstrate that the proposed method can not only outperform existing DDL but also state-of-the-art generic CNNs.

Conquering the CNN Over-Parameterization Dilemma: A Volterra Filtering Approach for Action Recognition

The importance of inference in Machine Learning (ML) has led to an explosive number of different proposals in ML, and particularly in Deep Learning. In an attempt to reduce the complexity of Convolutional Neural Networks, we propose a Volterra filter-inspired Network architecture. This architecture introduces controlled non-linearities in the form of interactions between the delayed input samples of data. We propose a cascaded implementation of Volterra Filter so as to significantly reduce the number of parameters required to carry out the same classification task as that of a conventional Neural Network. We demonstrate an efficient parallel implementation of this new Volterra network, along with its remarkable performance while retaining a relatively simpler and potentially more tractable structure. Furthermore, we show a rather sophisticated adaptation of this network to nonlinearly fuse the RGB (spatial) information and the Optical Flow (temporal) information of a video sequence for action recognition. The proposed approach is evaluated on UCF-101 and HMDB-51 datasets for action recognition, and is shown to outperform state of the art when trained on the datasets from scratch (i.e. without pre-training on a larger dataset).

Deep Adversarial Belief Networks

We present a novel adversarial framework for training deep belief networks (DBNs), which includes replacing the generator network in the methodology of generative adversarial networks (GANs) with a DBN and developing a highly parallelizable numerical algorithm for training the resulting architecture in a stochastic manner. Unlike the existing techniques, this framework can be applied to the most general form of DBNs with no requirement for back propagation. As such, it lays a new foundation for developing DBNs on a par with GANs with various regularization units, such as pooling and normalization. Foregoing back-propagation, our framework also exhibits superior scalability as compared to other DBN and GAN learning techniques. We present a number of numerical experiments in computer vision as well as neurosciences to illustrate the main advantages of our approach.