Optimization algorithms for inference and classification of genetic profiles from undersampled measurements

In this thesis, we tackle three different problems, all related to optimization techniques for inference and classification of genetic profiles. First, we extend the deterministic Non-negative Matrix Factorization (NMF) framework to the probabilistic case (PNMF). We apply the PNMF algorithm to cluster and classify DNA microarrays data. The proposed PNMF is shown to outperform the deterministic NMF and the sparse NMF algorithms in clustering stability and classification accuracy. Second, we propose SMURC: Small-sample MUltivariate Regression with Covariance estimation. Specifically, we consider a high dimension low sample-size multivariate regression problem that accounts for correlation of the response variables. We show that, in this case, the maximum likelihood approach is senseless because the likelihood diverges. We propose a normalization of the likelihood function that guarantees convergence. Simulation results show that SMURC outperforms the regularized likelihood estimator with known covariance matrix and the state-of-the-art sparse Conditional Graphical Gaussian Model (sCGGM). In the third Chapter, we derive a new greedy algorithm that provides an exact sparse solution of the combinatorial l sub zero-optimization problem in an exponentially less computation time. Unlike other greedy approaches, which are only approximations of the exact sparse solution, the proposed greedy approach, called Kernel reconstruction, leads to the exact optimal solution

Kernel Reconstruction: an Exact Greedy Algorithm for Compressive Sensing

Abstract-Compressive sensing is the theory of sparse signal recovery from undersampled measurements or observations. Exact signal reconstruction is an NP hard problem. A convex approximation using the l1-norm has received a great deal of theoretical attention. Exact recovery using the l1 approximation is only possible under strict conditions on the measurement matrix, which are difficult to check. Many greedy algorithms have thus been proposed. However, none of them is guaranteed to lead to the optimal (sparsest) solution. In this paper, we present a new greedy algorithm that provides an exact sparse solution of the problem. Unlike other greedy approaches, which are only approximations of the exact sparse solution, the proposed greedy approach, called Kernel Reconstruction, leads to the exact optimal solution in less operations than the original combinatorial problem. An application to the recovery of sparse gene regulatory networks is presented

Deep Learning Techniques For Multimedia Forensics

Digital images play an important role in a wide variety of settings such as news reporting, criminal investigations, etc. As a result, it is necessary to devise forensic algorithms capable of determining the source camera and the processing history of digital images. This is possible because both image editing operations and an image's source camera leave behind unique statistical traces in the same way that a criminal leaves behind fingerprints at a crime scene. Previous forensic techniques identify these fingerprints through theoretical analysis or develop heuristic features to capture their effects. These methods have their drawbacks where theoretical analysis is not always achievable and heuristic based approaches are often suboptimal. Recently, convolutional neural networks (CNNs) have gained significant attention due to their ability to adaptively learn classification features directly from data. While a forensic analyst can use CNNs to learn forensic fingerprints, this is problematic because CNNs in their standard form tend to learn features related to an image's content as opposed to learn forensic fingerprints which are content-independent. Thus, a forensic analyst must adapt the CNN to capture forensic fingerprints from images. To do this, they must develop new CNN architectures for different forensic tasks such as camera model identification and image editing detection. Additionally, CNNs in forensics must be robust to common post-processing operations which significantly deteriorate the performance of the existing forensic algorithms. Unfortunately, techniques from computer vision to increase CNN's robustness are not effective when designing and training forensic CNNs. As a result, new techniques must be developed to design and train forensic CNNs such that they are robust enough to operate in realistic scenarios. In this dissertation, we propose a set of new deep learning approaches to perform several multimedia forensic tasks. We first develop a new type of convolutional layer within a CNN, called a `constrained convolutional layer', that can jointly suppress an image's content and adaptively learn low-level forensic classification features directly from data. The constrained CNN has proven effective at performing image manipulation detection, order of processing operations detection, image manipulation parameter estimation, and camera model feature extraction for unknown classes detection. Next, we propose the architectural design guidelines to build a new CNN architecture associated with a forensic data augmentation based training method that can capture camera's traces in post-processed color images. We demonstrate the advantage of our approach over the existing forensic methods at identifying camera models in post-processed color images through rigorous experiments and analysis.Ph.D., Electrical Engineering -- Drexel University, 201

Exploiting Prediction Error Inconsistencies through LSTM-based Classifiers to Detect Deepfake Videos

The ability of artificial intelligence techniques to build synthesized brand new videos or to alter the facial expression of already existing ones has been efficiently demonstrated in the literature. The identification of such new threat generally known as Deepfake, but consisting of different techniques, is fundamental in multimedia forensics. In fact this kind of manipulated information could undermine and easily distort the public opinion on a certain person or about a specific event. Thus, in this paper, a new technique able to distinguish synthetic generated portrait videos from natural ones is introduced by exploiting inconsistencies due to the prediction error in the re-encoding phase. In particular, features based on inter-frame prediction error have been investigated jointly with a Long Short-Term Memory (LSTM) model network able to learn the temporal correlation among consecutive frames. Preliminary results have demonstrated that such sequence-based approach, used to distinguish between original and manipulated videos, highlights promising performances