The Incomplete Rosetta Stone Problem: Identifiability Results for Multi-View Nonlinear ICA

We consider the problem of recovering a common latent source with independent components from multiple views. This applies to settings in which a variable is measured with multiple experimental modalities, and where the goal is to synthesize the disparate measurements into a single unified representation. We consider the case that the observed views are a nonlinear mixing of component-wise corruptions of the sources. When the views are considered separately, this reduces to nonlinear Independent Component Analysis (ICA) for which it is provably impossible to undo the mixing. We present novel identifiability proofs that this is possible when the multiple views are considered jointly, showing that the mixing can theoretically be undone using function approximators such as deep neural networks. In contrast to known identifiability results for nonlinear ICA, we prove that independent latent sources with arbitrary mixing can be recovered as long as multiple, sufficiently different noisy views are available

Fourier PCA and Robust Tensor Decomposition

Fourier PCA is Principal Component Analysis of a matrix obtained from higher order derivatives of the logarithm of the Fourier transform of a distribution.We make this method algorithmic by developing a tensor decomposition method for a pair of tensors sharing the same vectors in rank-$1$ decompositions. Our main application is the first provably polynomial-time algorithm for underdetermined ICA, i.e., learning an $n \times m$ matrix $A$ from observations $y=Ax$ where $x$ is drawn from an unknown product distribution with arbitrary non-Gaussian components. The number of component distributions $m$ can be arbitrarily higher than the dimension $n$ and the columns of $A$ only need to satisfy a natural and efficiently verifiable nondegeneracy condition. As a second application, we give an alternative algorithm for learning mixtures of spherical Gaussians with linearly independent means. These results also hold in the presence of Gaussian noise.Comment: Extensively revised; details added; minor errors corrected; exposition improve

Advances in Latent Variable and Causal Models

This thesis considers three different areas of machine learning concerned with the modelling of data, extending theoretical understanding in each of them. First, the estimation of f- divergences is considered in a setting that is naturally satisfied in the context of autoencoders. By exploiting structural assumptions on the distributions of concern, the proposed estimator is shown to exhibit fast rates of concentration and bias-decay. In contrast, in much of the existing f-divergence estimation literature, fast rates are only obtainable under strong conditions that are difficult to verify in practice. Next, novel identifiability results are presented for nonlinear Independent Component Analysis (ICA) in a multi-view setting, extending the scarce literature of known identifiability results for nonlinear ICA. A result of particular note is that if one noiseless view of the sources is supplemented by a second view that is appropriately corrupted by source-level noise, the sources can be fully reconstructed from the observations up to tolerable ambiguities. This setting is applicable to areas such as neuroimaging, where multiple data modalities may be available. Finally, a framework is introduced to evaluate when two causal models are consistent with one another, meaning that a correspondence can be established between them such that reasoning about the effects of interventions in both models agree. This can be used to understand when two models of the same system at different levels of detail are consistent, and has application to the problem of causal variable definition. This work has broad implications to the causal modelling process in general, as there is often a mismatch between the level at which measurements are made and the level at which the underlying ‘true’ causal structure exists, yet causal inference algorithms generally seek to discover causal structure at the level of measurements

Data hiding in multimedia - theory and applications

Multimedia data hiding or steganography is a means of communication using subliminal channels. The resource for the subliminal communication scheme is the distortion of the original content that can be tolerated. This thesis addresses two main issues of steganographic communication schemes: 1. How does one maximize the distortion introduced without affecting fidelity of the content? 2. How does one efficiently utilize the resource (the distortion introduced) for communicating as many bits of information as possible? In other words, what is a good signaling strategy for the subliminal communication scheme? Close to optimal solutions for both issues are analyzed. Many techniques for the issue for maximizing the resource, viz, the distortion introduced imperceptibly in images and video frames, are proposed. Different signaling strategies for steganographic communication are explored, and a novel signaling technique employing a floating signal constellation is proposed. Algorithms for optimal choices of the parameters of the signaling technique are presented. Other application specific issues like the type of robustness needed are taken into consideration along with the established theoretical background to design optimal data hiding schemes. In particular, two very important applications of data hiding are addressed - data hiding for multimedia content delivery, and data hiding for watermarking (for proving ownership). A robust watermarking protocol for unambiguous resolution of ownership is proposed

Learning Identifiable Representations: Independent Influences and Multiple Views

Intelligent systems, whether biological or artificial, perceive unstructured information from the world around them: deep neural networks designed for object recognition receive collections of pixels as inputs; living beings capture visual stimuli through photoreceptors that convert incoming light into electrical signals. Sophisticated signal processing is required to extract meaningful features (e.g., the position, dimension, and colour of objects in an image) from these inputs: this motivates the field of representation learning. But what features should be deemed meaningful, and how to learn them? We will approach these questions based on two metaphors. The first one is the cocktail-party problem, where a number of conversations happen in parallel in a room, and the task is to recover (or separate) the voices of the individual speakers from recorded mixtures—also termed blind source separation. The second one is what we call the independent-listeners problem: given two listeners in front of some loudspeakers, the question is whether, when processing what they hear, they will make the same information explicit, identifying similar constitutive elements. The notion of identifiability is crucial when studying these problems, as it specifies suitable technical assumptions under which representations are uniquely determined, up to tolerable ambiguities like latent source reordering. A key result of this theory is that, when the mixing is nonlinear, the model is provably non-identifiable. A first question is, therefore, under what additional assumptions (ideally as mild as possible) the problem becomes identifiable; a second one is, what algorithms can be used to estimate the model. The contributions presented in this thesis address these questions and revolve around two main principles. The first principle is to learn representation where the latent components influence the observations independently. Here the term “independently” is used in a non-statistical sense—which can be loosely thought of as absence of fine-tuning between distinct elements of a generative process. The second principle is that representations can be learned from paired observations or views, where mixtures of the same latent variables are observed, and they (or a subset thereof) are perturbed in one of the views—also termed multi-view setting. I will present work characterizing these two problem settings, studying their identifiability and proposing suitable estimation algorithms. Moreover, I will discuss how the success of popular representation learning methods may be explained in terms of the principles above and describe an application of the second principle to the statistical analysis of group studies in neuroimaging

Structural and functional MRI study in mentally ill persons considered socially dangerous with diminished penal responsibility

La complessa relazione tra malattia mentale e criminalità rappresenta un tema di concreta rilevanza sociale, dibattuto da anni ma sempre di grande attualità. Secondo il codice penale, è considerato “socialmente pericoloso” il soggetto autore di reato, anche se non imputabile per vizio totale o parziale di mente, che abbia una elevata probabilità di recidiva del reato. Per questo motivo la prevenzione delle azioni socialmente pericolose riveste un ruolo di fondamentale importanza giuridica e sociale. In questo contesto la psichiatria forense si occupa delle questioni che sorgono all’interfaccia tra psichiatria e giurisprudenza, con l’obiettivo principale di evidenziare lo stato di salute mentale dei soggetti che commettono un reato attraverso una perizia psichiatrica. La disciplina neuroradiologica, grazie anche all’utilizzo di tecniche avanzate di analisi delle immagini, si pone oggi come strumento di valido ausilio nella valutazione clinica dei pazienti psichiatrici e può supportare gli sforzi congiunti di psichiatri e giuristi per studiare la relazione tra malattia mentale e criminalità. L’obiettivo di questo progetto di dottorato è stato quello di effettuare uno studio volumetrico della sostanza grigia cerebrale attraverso un esame di Risonanza Magnetica (RM) su un gruppo di soggetti autori di reato, considerati non imputabili al momento del fatto per vizio totale o parziale di mente, detenuti nella REMS dell’ASL Rm5 e considerati socialmente pericolosi. I risultati dell’analisi volumetrica sono stati confrontati con un gruppo di controllo, comparabile per età e sesso. E’stata inoltre effettuata un’analisi della connettività funzionale cerebrale a riposo (resting-state functional MRI) con l’intento di indagare i network cerebrali alla base del comportamento morale, dell’attribuzione della salienza e dei processi di ricompensa, confrontando sempre i risultati con un gruppo di controllo. Nel gruppo sperimentale sono stati inclusi 13 individui destrorsi (età media: 44 ± 7 anni) detenuti nella REMS dell’ASL Rm5 con disturbo dello spettro psicotico (schizofrenia, disturbo bipolare con caratteristiche psicotiche, disturbo schizo-affettivo, disturbi deliranti), che hanno commesso crimini violenti (omicidi, tentati omicidi, aggressioni e violenze domestiche) e che sono stati dichiarati socialmente pericolosi dall’autorità giudiziaria a causa dell’ alto rischio di recidiva criminale. I dati di RM sono stati acquisiti su un magnete 3 Tesla (Verio, Siemens) dotato di una bobina a 12 canali, utilizzando sequenze volumetriche T13D e sequenze BOLD eco-planari (EPI). Nello studio I abbiamo eseguito un’analisi della volumetria cerebrale con tecnica VBM (Voxel-based morphometry) utilizzando il Computational Anatomy Toolbox (CAT12) del software Statistical Parametric Mapping (SPM12). Abbiamo riscontrato come il volume della sostanza grigia cerebrale del gruppo sperimentale fosse significativamente ridotto, rispetto ai controlli, a livello della corteccia insulare bilaterale, nel giro temporale superiore (STG) dell’emisfero sinistro e nel giro fusiforme dell’emisfero destro. Abbiamo infine eseguito un’analisi di correlazione tra la gravità dei sintomi psichiatrici e le regioni con volume corticale ridotto. I cluster di volume a livello di STG e insula sinistra sono risultati essere significativamente correlati alla gravità dei sintomi espressa dalla scala di valutazione BPRS (Brief Psychiatric Rating Scale). Nello studio II abbiamo esaminato la connettività cerebrale a riposo nelle 19 regioni selezionate “a priori” sulla base della letteratura che risultassero coinvolte nella morale, nell’ attribuzione della salienza e nei processi di ricompensa. L’analisi è stata effettuata utilizzando il software CONN v. 18a, sulla piattaforma Matlab. Abbiamo documentato una ridotta connettività tra le regioni del sistema limbico, come il nucleo accumbens e l’amigdala, ed aumentata connettività nello striato dorsale, tra il nucleo accumbens e la corteccia cingolata posteriore, tra corteccia fronto-orbitale e gangli della base e tra corteccia cingolata anteriore e amigdala. Sulla base di questi risultati ipotizziamo che l’alterata connettività in queste specifiche aree possa rappresentare la modificazione del comportamento in senso maladattativo degli individui del gruppo sperimentale, in termini di alterata risposta emotiva circa le proprie violazioni morali o di mancanza di empatia verso gli altri al fine di ottenere vantaggi personali o riguardo al controllo dell’impulsività. Nonostante la bassa numerosità campionaria non consenta di approdare a conclusioni definitive, questo studio cerca di approfondire i correlati neurali degli individui autori di reato con ridotta responsabilità penale e socialmente pericolosi al fine di fornire un eventuale strumento di ausilio nella valutazione di questa particolare categoria di persone, con importanti risvolti giuridici ed etici oltre che nella pianificazione e nello sviluppo del trattamento di questi pazienti durante la loro permanenza nelle REMS.The relation between mental illness and criminality is a relevant social issue that has been debated over the years. Socially dangerous actions committed by mentally ill patients often have severe consequences, which is why much public attention is directed toward the prevention of these actions by these individuals. Modern neuroimaging investigations support the joint efforts of psychiatrists and lawyers to study the relationship between psychiatric illness and criminality. The overall aim of this PhD project was to investigate differences in cortical GM volumes of this population, compared to a control group of healthy non-offender participants, using a VBM analysis of structural MRI. We also decided to investigate brain networks underpinning moral behaviour, salience attribution and reward processes performing a functional MRI at resting-state. Experimental Group (EG) included 13 right-handed individuals (mean age: 44 ± 7 yrs) who committed violent crimes (homicides, attempted homicides, aggressions, and domestic violence), had a diagnosis included in the psychotic spectrum (schizophrenia, bipolar disorder with psychotic features, schizoaffective disorder, delusional disorders) and were declared socially dangerous by the judicial authority due to a high risk of criminal recidivism. All subjects of the EG were institutionalized in the REMS psychiatric unit of ASL RM5 (Rome, Italy) for no longer than two years. Thirteen healthy right-handed men, who had never received a psychiatric diagnosis, undergone any psychiatric treatment, or been convicted of any crime were included in the control group (CG) (mean age: 38 ± 11yrs). MRI data were acquired using a 3 Tesla Siemens imaging system (Siemens, Verio, Erlangen, Germany) equipped with a 12-channel head coil. Structural scans of the brain were acquired for each participant using a T1-weighted three dimensionals sagittal magnetization-prepared rapid gradient echo sequence. Resting state functional (rs-fMRI) data were collected while participants lay still and awake, with eyes closed using T2*-weighted gradient-echo echo-planar functional images (EPIs). In study I we performed a voxel-based morphometry (VBM) analyses on participants’ T1-weighted structural images using Computational Anatomy Toolbox (CAT12), which runs within SPM12. We found that total cerebral GM volume was significantly reduced in EG in specific regions within the bilateral insular cortex compared to controls. We also found a reduced GM volume in the superior temporal gyrus (STG) of left hemisphere and in the fusiform gyrus of the right hemisphere. We finally performed a correlation analyses between psychiatric symptoms and regions with reduced GM volume. The clusters in STG and insula of left hemisphere significantly correlated with the gravity of symptoms expressed by the BPRS (Brief Psychiatric Rating Scale). In study II, temporal correlations of the resting-state BOLD signal time series were examined between nineteen seed regions that we selected “a priori” among those known to be involved in moral judgment salience attribution and reward processes. Analysis was performed using the software CONN v. 18a, running in Matlab. Our results documented reduced connectivity in limbic regions like the nucleus accumbens and the amiygdala and augmented connectivity within the dorsal striatum, between nucleus accumbens and the posterior cingulate cortex, between fronto- orbitalis cortex and basal ganglia and anterior cingulate cortex and amygdala. We suggest that dysregulation in these areas reflects the maladaptive behavior of socially dangerous subjects in terms of an altered emotional response to their own moral violations and a lack of empathy for others when making personal desire-oriented decisions. While the small sample size does not allow definitive conclusions to be reached, the present study sheds some light on the neural correlates of this specific population, which deserves further attention due to their theoretical and clinical implications. A further understanding of the neural basis of risk evaluation in mentally ill persons with a history of violence who are judged not criminally responsible could aid in forensic assessment and treatment development

Personal imaging

Thesis (Ph.D.)--Massachusetts Institute of Technology, School of Architecture and Planning, Program in Media Arts & Sciences, 1997.Includes bibliographical references (p. 217-223).In this thesis, I propose a new synergy between humans and computers, called "Humanistic Intelligence" (HI), and provide a precise definition of this new form of human-computer interaction. I then present a means and apparatus for reducing this principle to practice. The bulk of this thesis concentrates on a specific embodiment of this invention, called Personal Imaging, most notably, a system which I show attains new levels of creativity in photography, defines a new genre of documentary video, and goes beyond digital photography/video to define a new renaissance in imaging, based on simple principles of projective geometry combined with linearity and superposition properties of light. I first present a mathematical theory of imaging which allows the apparatus to measure, to within a single unknown constant, the quantity of light arriving from each direction, to a fixed point in space, using a collection of images taken from a sensor array having a possibly unknown nonlinearity. Within the context of personal imaging, this theory is a contribution in and of itself (in the sense that it was an unsolved problem previously), but when also combined with the proposed apparatus, it allows one to construct environment maps by simply looking around. I then present a new form of connected humanistic intelligence in which individuals can communicate, across boundaries of time and space, using shared environment maps, and the resulting computer-mediated reality that arises out of long-term adaptation in a personal imaging environment. Finally, I present a new philosophical framework for cultural criticism which arises out of a new concept called 'humanistic property'. This new philosophical framework has two axes, a 'reflectionist' axis and a 'diffusionist' axis. In particular, I apply the new framework to personal imaging, thus completing a body of work that lies at the intersection of art, science, and technology.by Steve Mann.Ph.D

Motion Segmentation Aided Super Resolution Image Reconstruction

This dissertation addresses Super Resolution (SR) Image Reconstruction focusing on motion segmentation. The main thrust is Information Complexity guided Gaussian Mixture Models (GMMs) for Statistical Background Modeling. In the process of developing our framework we also focus on two other topics; motion trajectories estimation toward global and local scene change detections and image reconstruction to have high resolution (HR) representations of the moving regions. Such a framework is used for dynamic scene understanding and recognition of individuals and threats with the help of the image sequences recorded with either stationary or non-stationary camera systems. We introduce a new technique called Information Complexity guided Statistical Background Modeling. Thus, we successfully employ GMMs, which are optimal with respect to information complexity criteria. Moving objects are segmented out through background subtraction which utilizes the computed background model. This technique produces superior results to competing background modeling strategies. The state-of-the-art SR Image Reconstruction studies combine the information from a set of unremarkably different low resolution (LR) images of static scene to construct an HR representation. The crucial challenge not handled in these studies is accumulating the corresponding information from highly displaced moving objects. In this aspect, a framework of SR Image Reconstruction of the moving objects with such high level of displacements is developed. Our assumption is that LR images are different from each other due to local motion of the objects and the global motion of the scene imposed by non-stationary imaging system. Contrary to traditional SR approaches, we employed several steps. These steps are; the suppression of the global motion, motion segmentation accompanied by background subtraction to extract moving objects, suppression of the local motion of the segmented out regions, and super-resolving accumulated information coming from moving objects rather than the whole scene. This results in a reliable offline SR Image Reconstruction tool which handles several types of dynamic scene changes, compensates the impacts of camera systems, and provides data redundancy through removing the background. The framework proved to be superior to the state-of-the-art algorithms which put no significant effort toward dynamic scene representation of non-stationary camera systems

Visibility recovery on images acquired in attenuating media. Application to underwater, fog, and mammographic imaging

136 p.When acquired in attenuating media, digital images of ten suffer from a particularly complex degradation that reduces their visual quality, hindering their suitability for further computational applications, or simply decreasing the visual pleasan tness for the user. In these cases, mathematical image processing reveals it self as an ideal tool to recover some of the information lost during the degradation process. In this dissertation,we deal with three of such practical scenarios in which this problematic is specially relevant, namely, underwater image enhancement, fogremoval and mammographic image processing. In the case of digital mammograms,X-ray beams traverse human tissue, and electronic detectorscapture them as they reach the other side. However, the superposition on a bidimensional image of three-dimensional structures produces low contraste dimages in which structures of interest suffer from a diminished visibility, obstructing diagnosis tasks. Regarding fog removal, the loss of contrast is produced by the atmospheric conditions, and white colour takes over the scene uniformly as distance increases, also reducing visibility.For underwater images, there is an added difficulty, since colour is not lost uniformly; instead, red colours decay the fastest, and green and blue colours typically dominate the acquired images. To address all these challenges,in this dissertation we develop new methodologies that rely on: a)physical models of the observed degradation, and b) the calculus of variations.Equipped with this powerful machinery, we design novel theoreticaland computational tools, including image-dependent functional energies that capture the particularities of each degradation model. These energie sare composed of different integral terms that are simultaneous lyminimized by means of efficient numerical schemes, producing a clean,visually-pleasant and use ful output image, with better contrast and increased visibility. In every considered application, we provide comprehensive qualitative (visual) and quantitative experimental results to validateour methods, confirming that the developed techniques out perform other existing approaches in the literature