Learning Causally Disentangled Representations via the Principle of Independent Causal Mechanisms

Learning disentangled causal representations is a challenging problem that has gained significant attention recently due to its implications for extracting meaningful information for downstream tasks. In this work, we define a new notion of causal disentanglement from the perspective of independent causal mechanisms. We propose ICM-VAE, a framework for learning causally disentangled representations supervised by causally related observed labels. We model causal mechanisms using learnable flow-based diffeomorphic functions to map noise variables to latent causal variables. Further, to promote the disentanglement of causal factors, we propose a causal disentanglement prior that utilizes the known causal structure to encourage learning a causally factorized distribution in the latent space. Under relatively mild conditions, we provide theoretical results showing the identifiability of causal factors and mechanisms up to permutation and elementwise reparameterization. We empirically demonstrate that our framework induces highly disentangled causal factors, improves interventional robustness, and is compatible with counterfactual generation

TCGM: An Information-Theoretic Framework for Semi-Supervised Multi-Modality Learning

Fusing data from multiple modalities provides more information to train machine learning systems. However, it is prohibitively expensive and time-consuming to label each modality with a large amount of data, which leads to a crucial problem of semi-supervised multi-modal learning. Existing methods suffer from either ineffective fusion across modalities or lack of theoretical guarantees under proper assumptions. In this paper, we propose a novel information-theoretic approach, namely \textbf{T}otal \textbf{C}orrelation \textbf{G}ain \textbf{M}aximization (TCGM), for semi-supervised multi-modal learning, which is endowed with promising properties: (i) it can utilize effectively the information across different modalities of unlabeled data points to facilitate training classifiers of each modality (ii) it has theoretical guarantee to identify Bayesian classifiers, i.e., the ground truth posteriors of all modalities. Specifically, by maximizing TC-induced loss (namely TC gain) over classifiers of all modalities, these classifiers can cooperatively discover the equivalent class of ground-truth classifiers; and identify the unique ones by leveraging limited percentage of labeled data. We apply our method to various tasks and achieve state-of-the-art results, including news classification, emotion recognition and disease prediction.Comment: ECCV 2020 (oral

Variational Inference for Text Generation: Improving the Posterior

Learning useful representations of data is a crucial task in machine learning with wide ranging applications. In this thesis we explore improving representations of models based on variational inference by improving the posterior. We explore two approaches towards this goal: 1) auxiliary losses to regularize the latent space and enforcing desired properties and 2) normalizing flows to develop more flexible posteriors to be used during variational inference. We propose a proximity based loss function that helps in disentanglement by regularizing the latent space based on similarity according to a criterion. We evaluate our model on a task of disentangling semantics and syntax in sentences and empirically show that our model successfully manages to learn independent subspaces that learn semantics and syntax respectively. We compare our model to existing approaches using automated metrics and human evaluation to show that our model is competitive. We also explore the effectiveness of normalizing flows for representation learning and generative modeling. We perform experiments that empirically show that variational inference with normalizing flows beats standard approaches based on simple posteriors across various metrics in text generation and language modeling. We also propose a variant of planar normalizing flows called block planar normalizing flows for use in disentanglement tasks. We perform ablation experiments to empirically show that our proposed block planar flows help in improving disentanglement

Human-controllable and structured deep generative models

Deep generative models are a class of probabilistic models that attempts to learn the underlying data distribution. These models are usually trained in an unsupervised way and thus, do not require any labels. Generative models such as Variational Autoencoders and Generative Adversarial Networks have made astounding progress over the last years. These models have several benefits: eased sampling and evaluation, efficient learning of low-dimensional representations for downstream tasks, and better understanding through interpretable representations. However, even though the quality of these models has improved immensely, the ability to control their style and structure is limited. Structured and human-controllable representations of generative models are essential for human-machine interaction and other applications, including fairness, creativity, and entertainment. This thesis investigates learning human-controllable and structured representations with deep generative models. In particular, we focus on generative modelling of 2D images. For the first part, we focus on learning clustered representations. We propose semi-parametric hierarchical variational autoencoders to estimate the intensity of facial action units. The semi-parametric model forms a hybrid generative-discriminative model and leverages both parametric Variational Autoencoder and non-parametric Gaussian Process autoencoder. We show superior performance in comparison with existing facial action unit estimation approaches. Based on the results and analysis of the learned representation, we focus on learning Mixture-of-Gaussians representations in an autoencoding framework. We deviate from the conventional autoencoding framework and consider a regularized objective with the Cauchy-Schwarz divergence. The Cauchy-Schwarz divergence allows a closed-form solution for Mixture-of-Gaussian distributions and, thus, efficiently optimizing the autoencoding objective. We show that our model outperforms existing Variational Autoencoders in density estimation, clustering, and semi-supervised facial action detection. We focus on learning disentangled representations for conditional generation and fair facial attribute classification for the second part. Conditional image generation relies on the accessibility to large-scale annotated datasets. Nevertheless, the geometry of visual objects, such as in faces, cannot be learned implicitly and deteriorate image fidelity. We propose incorporating facial landmarks with a statistical shape model and a differentiable piecewise affine transformation to separate the representation for appearance and shape. The goal of incorporating facial landmarks is that generation is controlled and can separate different appearances and geometries. In our last work, we use weak supervision for disentangling groups of variations. Works on learning disentangled representation have been done in an unsupervised fashion. However, recent works have shown that learning disentangled representations is not identifiable without any inductive biases. Since then, there has been a shift towards weakly-supervised disentanglement learning. We investigate using regularization based on the Kullback-Leiber divergence to disentangle groups of variations. The goal is to have consistent and separated subspaces for different groups, e.g., for content-style learning. Our evaluation shows increased disentanglement abilities and competitive performance for image clustering and fair facial attribute classification with weak supervision compared to supervised and semi-supervised approaches.Open Acces

Optimal transport for Latent variable models

Generative models are probabilistic models which aim at approximating the process by which a given dataset is generated. They are well suited to the unsupervised learning setup and constitute intuitive and powerful models providing an interpretable representation of the data. However, learning even simple generative models can be challenging in the traditional Maximum Likelihood framework, due to the inflexibility of the training objective used. Motivated by its topological properties, we will show in this thesis how methods based on Optimal Transport can overcome these difficulties and offer competitive alternatives. Firstly, we show that training generative models that combine both discrete and continuous latent variables can be significantly more effective when using Optimal Transport methods. Such intuitive models are highly motivated by the structure of many real-world datasets but remain hard to train with the most common likelihood-based method, often resulting in the collapse of the discrete latent variables. Secondly, we propose a novel approach based on Optimal Transport to training models with fully Markovian deep-latent hierarchies. Probabilistic models with deep latent-variable structures have powerful modelling capacity, but common approaches often fail to leverage deep-latent hierarchies without complex inference and optimisation schemes. Our method successfully leverages the whole hierarchy of the models and shows competitive generative performance while learning smooth latent manifolds through every layers of the latent hierarchy. Finally, we introduce a new training objective to improve the learning of interpretable and disentangled representation of the data. Our method achieves competitive disentanglement relative to state-of-the-art techniques whilst improving the reconstruction and generation performances of the models

Advances in identifiability of nonlinear probabilistic models

Identifiability is a highly prized property of statistical models. This thesis investigates this property in nonlinear models encountered in two fields of statistics: representation learning and causal discovery. In representation learning, identifiability leads to learning interpretable and reproducible representations, while in causal discovery, it is necessary for the estimation of correct causal directions. We begin by leveraging recent advances in nonlinear ICA to show that the latent space of a VAE is identifiable up to a permutation and pointwise nonlinear transformations of its components. A factorized prior distribution over the latent variables conditioned on an auxiliary observed variable, such as a class label or nearly any other observation, is required for our result. We also extend previous identifiability results in nonlinear ICA to the case of noisy or undercomplete observations, and incorporate them into a maximum likelihood framework. Our second contribution is to develop the Independently Modulated Component Analysis (IMCA) framework, a generalization of nonlinear ICA to non-independent latent variables. We show that we can drop the independence assumption in ICA while maintaining identifiability, resulting in a very flexible and generic framework for principled disentangled representation learning. This finding is predicated on the existence of an auxiliary variable that modulates the joint distribution of the latent variables in a factorizable manner. As a third contribution, we extend the identifiability theory to a broad family of conditional energy-based models (EBMs). This novel model generalizes earlier results by removing any distributional assumptions on the representations, which are ubiquitous in the latent variable setting. The conditional EBM can learn identifiable overcomplete representations and has universal approximation capabilities/. Finally, we investigate a connection between the framework of autoregressive normalizing flow models and causal discovery. Causal models derived from affine autoregressive flows are shown to be identifiable, generalizing the wellknown additive noise model. Using normalizing flows, we can compute the exact likelihood of the causal model, which is subsequently used to derive a likelihood ratio measure for causal discovery. They are also invertible, making them perfectly suitable for performing causal inference tasks like interventions and counterfactuals

MANIFOLD REPRESENTATIONS OF MUSICAL SIGNALS AND GENERATIVE SPACES

Tra i diversi campi di ricerca nell\u2019ambito dell\u2019informatica musicale, la sintesi e la generazione di segnali audio incarna la pluridisciplinalita\u300 di questo settore, nutrendo insieme le pratiche scientifiche e musicale dalla sua creazione. Inerente all\u2019informatica dalla sua creazione, la generazione audio ha ispirato numerosi approcci, evolvendo colle pratiche musicale e gli progressi tecnologici e scientifici. Inoltre, alcuni processi di sintesi permettono anche il processo inverso, denominato analisi, in modo che i parametri di sintesi possono anche essere parzialmente o totalmente estratti dai suoni, dando una rappresentazione alternativa ai segnali analizzati. Per di piu\u300, la recente ascesa dei algoritmi di l\u2019apprendimento automatico ha vivamente interrogato il settore della ricerca scientifica, fornendo potenti data-centered metodi che sollevavano diversi epistemologici interrogativi, nonostante i sui efficacia. Particolarmente, un tipo di metodi di apprendimento automatico, denominati modelli generativi, si concentrano sulla generazione di contenuto originale usando le caratteristiche che hanno estratti dei dati analizzati. In tal caso, questi modelli non hanno soltanto interrogato i precedenti metodi di generazione, ma anche sul modo di integrare questi algoritmi nelle pratiche artistiche. Mentre questi metodi sono progressivamente introdotti nel settore del trattamento delle immagini, la loro applicazione per la sintesi di segnali audio e ancora molto marginale. In questo lavoro, il nostro obiettivo e di proporre un nuovo metodo di audio sintesi basato su questi nuovi tipi di generativi modelli, rafforazti dalle nuove avanzati dell\u2019apprendimento automatico. Al primo posto, facciamo una revisione dei approcci esistenti nei settori dei sistemi generativi e di sintesi sonore, focalizzando sul posto di nostro lavoro rispetto a questi disciplini e che cosa possiamo aspettare di questa collazione. In seguito, studiamo in maniera piu\u300 precisa i modelli generativi, e come possiamo utilizzare questi recenti avanzati per l\u2019apprendimento di complesse distribuzione di suoni, in un modo che sia flessibile e nel flusso creativo del utente. Quindi proponiamo un processo di inferenza / generazione, il quale rifletta i processi di analisi/sintesi che sono molto usati nel settore del trattamento del segnale audio, usando modelli latenti, che sono basati sull\u2019utilizzazione di un spazio continuato di alto livello, che usiamo per controllare la generazione. Studiamo dapprima i risultati preliminari ottenuti con informazione spettrale estratte da diversi tipi di dati, che valutiamo qualitativamente e quantitativamente. Successiva- mente, studiamo come fare per rendere questi metodi piu\u300 adattati ai segnali audio, fronteggiando tre diversi aspetti. Primo, proponiamo due diversi metodi di regolarizzazione di questo generativo spazio che sono specificamente sviluppati per l\u2019audio : una strategia basata sulla traduzione segnali / simboli, e una basata su vincoli percettivi. Poi, proponiamo diversi metodi per fronteggiare il aspetto temporale dei segnali audio, basati sull\u2019estrazione di rappresentazioni multiscala e sulla predizione, che permettono ai generativi spazi ottenuti di anche modellare l\u2019aspetto dinamico di questi segnali. Per finire, cambiamo il nostro approccio scientifico per un punto di visto piu\u301 ispirato dall\u2019idea di ricerca e creazione. Primo, descriviamo l\u2019architettura e il design della nostra libreria open-source, vsacids, sviluppata per permettere a esperti o non-esperti musicisti di provare questi nuovi metodi di sintesi. Poi, proponiamo una prima utilizzazione del nostro modello con la creazione di una performance in real- time, chiamata \ue6go, basata insieme sulla nostra libreria vsacids e sull\u2019uso di une agente di esplorazione, imparando con rinforzo nel corso della composizione. Finalmente, tramo dal lavoro presentato alcuni conclusioni sui diversi modi di migliorare e rinforzare il metodo di sintesi proposto, nonche\u301 eventuale applicazione artistiche.Among the diverse research fields within computer music, synthesis and generation of audio signals epitomize the cross-disciplinarity of this domain, jointly nourishing both scientific and artistic practices since its creation. Inherent in computer music since its genesis, audio generation has inspired numerous approaches, evolving both with musical practices and scientific/technical advances. Moreover, some syn- thesis processes also naturally handle the reverse process, named analysis, such that synthesis parameters can also be partially or totally extracted from actual sounds, and providing an alternative representation of the analyzed audio signals. On top of that, the recent rise of machine learning algorithms earnestly questioned the field of scientific research, bringing powerful data-centred methods that raised several epistemological questions amongst researchers, in spite of their efficiency. Especially, a family of machine learning methods, called generative models, are focused on the generation of original content using features extracted from an existing dataset. In that case, such methods not only questioned previous approaches in generation, but also the way of integrating this methods into existing creative processes. While these new generative frameworks are progressively introduced in the domain of image generation, the application of such generative techniques in audio synthesis is still marginal. In this work, we aim to propose a new audio analysis-synthesis framework based on these modern generative models, enhanced by recent advances in machine learning. We first review existing approaches, both in sound synthesis and in generative machine learning, and focus on how our work inserts itself in both practices and what can be expected from their collation. Subsequently, we focus a little more on generative models, and how modern advances in the domain can be exploited to allow us learning complex sound distributions, while being sufficiently flexible to be integrated in the creative flow of the user. We then propose an inference / generation process, mirroring analysis/synthesis paradigms that are natural in the audio processing domain, using latent models that are based on a continuous higher-level space, that we use to control the generation. We first provide preliminary results of our method applied on spectral information, extracted from several datasets, and evaluate both qualitatively and quantitatively the obtained results. Subsequently, we study how to make these methods more suitable for learning audio data, tackling successively three different aspects. First, we propose two different latent regularization strategies specifically designed for audio, based on and signal / symbol translation and perceptual constraints. Then, we propose different methods to address the inner temporality of musical signals, based on the extraction of multi-scale representations and on prediction, that allow the obtained generative spaces that also model the dynamics of the signal. As a last chapter, we swap our scientific approach to a more research & creation-oriented point of view: first, we describe the architecture and the design of our open-source library, vsacids, aiming to be used by expert and non-expert music makers as an integrated creation tool. Then, we propose an first musical use of our system by the creation of a real-time performance, called aego, based jointly on our framework vsacids and an explorative agent using reinforcement learning to be trained during the performance. Finally, we draw some conclusions on the different manners to improve and reinforce the proposed generation method, as well as possible further creative applications.A\u300 travers les diffe\u301rents domaines de recherche de la musique computationnelle, l\u2019analysie et la ge\u301ne\u301ration de signaux audio sont l\u2019exemple parfait de la trans-disciplinarite\u301 de ce domaine, nourrissant simultane\u301ment les pratiques scientifiques et artistiques depuis leur cre\u301ation. Inte\u301gre\u301e a\u300 la musique computationnelle depuis sa cre\u301ation, la synthe\u300se sonore a inspire\u301 de nombreuses approches musicales et scientifiques, e\u301voluant de pair avec les pratiques musicales et les avance\u301es technologiques et scientifiques de son temps. De plus, certaines me\u301thodes de synthe\u300se sonore permettent aussi le processus inverse, appele\u301 analyse, de sorte que les parame\u300tres de synthe\u300se d\u2019un certain ge\u301ne\u301rateur peuvent e\u302tre en partie ou entie\u300rement obtenus a\u300 partir de sons donne\u301s, pouvant ainsi e\u302tre conside\u301re\u301s comme une repre\u301sentation alternative des signaux analyse\u301s. Paralle\u300lement, l\u2019inte\u301re\u302t croissant souleve\u301 par les algorithmes d\u2019apprentissage automatique a vivement questionne\u301 le monde scientifique, apportant de puissantes me\u301thodes d\u2019analyse de donne\u301es suscitant de nombreux questionnements e\u301piste\u301mologiques chez les chercheurs, en de\u301pit de leur effectivite\u301 pratique. En particulier, une famille de me\u301thodes d\u2019apprentissage automatique, nomme\u301e mode\u300les ge\u301ne\u301ratifs, s\u2019inte\u301ressent a\u300 la ge\u301ne\u301ration de contenus originaux a\u300 partir de caracte\u301ristiques extraites directement des donne\u301es analyse\u301es. Ces me\u301thodes n\u2019interrogent pas seulement les approches pre\u301ce\u301dentes, mais aussi sur l\u2019inte\u301gration de ces nouvelles me\u301thodes dans les processus cre\u301atifs existants. Pourtant, alors que ces nouveaux processus ge\u301ne\u301ratifs sont progressivement inte\u301gre\u301s dans le domaine la ge\u301ne\u301ration d\u2019image, l\u2019application de ces techniques en synthe\u300se audio reste marginale. Dans cette the\u300se, nous proposons une nouvelle me\u301thode d\u2019analyse-synthe\u300se base\u301s sur ces derniers mode\u300les ge\u301ne\u301ratifs, depuis renforce\u301s par les avance\u301es modernes dans le domaine de l\u2019apprentissage automatique. Dans un premier temps, nous examinerons les approches existantes dans le domaine des syste\u300mes ge\u301ne\u301ratifs, sur comment notre travail peut s\u2019inse\u301rer dans les pratiques de synthe\u300se sonore existantes, et que peut-on espe\u301rer de l\u2019hybridation de ces deux approches. Ensuite, nous nous focaliserons plus pre\u301cise\u301ment sur comment les re\u301centes avance\u301es accomplies dans ce domaine dans ce domaine peuvent e\u302tre exploite\u301es pour l\u2019apprentissage de distributions sonores complexes, tout en e\u301tant suffisamment flexibles pour e\u302tre inte\u301gre\u301es dans le processus cre\u301atif de l\u2019utilisateur. Nous proposons donc un processus d\u2019infe\u301rence / g\ue9n\ue9ration, refle\u301tant les paradigmes d\u2019analyse-synthe\u300se existant dans le domaine de ge\u301ne\u301ration audio, base\u301 sur l\u2019usage de mode\u300les latents continus que l\u2019on peut utiliser pour contro\u302ler la ge\u301ne\u301ration. Pour ce faire, nous e\u301tudierons de\u301ja\u300 les re\u301sultats pre\u301liminaires obtenus par cette me\u301thode sur l\u2019apprentissage de distributions spectrales, prises d\u2019ensembles de donne\u301es diversifie\u301s, en adoptant une approche a\u300 la fois quantitative et qualitative. Ensuite, nous proposerons d\u2019ame\u301liorer ces me\u301thodes de manie\u300re spe\u301cifique a\u300 l\u2019audio sur trois aspects distincts. D\u2019abord, nous proposons deux strate\u301gies de re\u301gularisation diffe\u301rentes pour l\u2019analyse de signaux audio : une base\u301e sur la traduction signal/ symbole, ainsi qu\u2019une autre base\u301e sur des contraintes perceptives. Nous passerons par la suite a\u300 la dimension temporelle de ces signaux audio, proposant de nouvelles me\u301thodes base\u301es sur l\u2019extraction de repre\u301sentations temporelles multi-e\u301chelle et sur une ta\u302che supple\u301mentaire de pre\u301diction, permettant la mode\u301lisation de caracte\u301ristiques dynamiques par les espaces ge\u301ne\u301ratifs obtenus. En dernier lieu, nous passerons d\u2019une approche scientifique a\u300 une approche plus oriente\u301e vers un point de vue recherche & cre\u301ation. Premie\u300rement, nous pre\u301senterons notre librairie open-source, vsacids, visant a\u300 e\u302tre employe\u301e par des cre\u301ateurs experts et non-experts comme un outil inte\u301gre\u301. Ensuite, nous proposons une premie\u300re utilisation musicale de notre syste\u300me par la cre\u301ation d\u2019une performance temps re\u301el, nomme\u301e \ue6go, base\u301e a\u300 la fois sur notre librarie et sur un agent d\u2019exploration appris dynamiquement par renforcement au cours de la performance. Enfin, nous tirons les conclusions du travail accompli jusqu\u2019a\u300 maintenant, concernant les possibles ame\u301liorations et de\u301veloppements de la me\u301thode de synthe\u300se propose\u301e, ainsi que sur de possibles applications cre\u301atives

Visual Processing and Latent Representations in Biological and Artificial Neural Networks

The human visual system performs the impressive task of converting light arriving at the retina into a useful representation that allows us to make sense of the visual environment. We can navigate easily in the three-dimensional world and recognize objects and their properties, even if they appear from different angles and under different lighting conditions. Artificial systems can also perform well on a variety of complex visual tasks. While they may not be as robust and versatile as their biological counterpart, they have surprising capabilities that are rapidly improving. Studying the two types of systems can help us understand what computations enable the transformation of low-level sensory data into an abstract representation. To this end, this dissertation follows three different pathways. First, we analyze aspects of human perception. The focus is on the perception in the peripheral visual field and the relation to texture perception. Our work builds on a texture model that is based on the features of a deep neural network. We start by expanding the model to the temporal domain to capture dynamic textures such as flames or water. Next, we use psychophysical methods to investigate quantitatively whether humans can distinguish natural textures from samples that were generated by a texture model. Finally, we study images that cover the entire visual field and test whether matching the local summary statistics can produce metameric images independent of the image content. Second, we compare the visual perception of humans and machines. We conduct three case studies that focus on the capabilities of artificial neural networks and the potential occurrence of biological phenomena in machine vision. We find that comparative studies are not always straightforward and propose a checklist on how to improve the robustness of the conclusions that we draw from such studies. Third, we address a fundamental discrepancy between human and machine vision. One major strength of biological vision is its robustness to changes in the appearance of image content. For example, for unusual scenarios, such as a cow on a beach, the recognition performance of humans remains high. This ability is lacking in many artificial systems. We discuss on a conceptual level how to robustly disentangle attributes that are correlated during training, and test this on a number of datasets