Causal discovery, i.e., inferring underlying causal relationships from observational data, is highly challenging for AI systems. In a time series modeling context, traditional causal discovery methods mainly consider constrained scenarios with fully observed variables and/or data from stationary time-series. We develop a causal discovery approach to handle a wide class of nonstationary time series that are conditionally stationary, where the nonstationary behaviour is modeled as stationarity conditioned on a set of latent state variables. Named State-Dependent Causal Inference (SDCI), our approach is able to recover the underlying causal dependencies, with provable identifiablity for the state-dependent causal structures. Empirical experiments on nonlinear particle interaction data and gene regulatory networks demonstrate SDCI’s superior performance over baseline causal discovery methods. Improved results over non-causal RNNs on modeling NBA player movements demonstrate the potential of our method and motivate the use of causality-driven methods for forecasting.

We introduce Matcha-TTS, a new encoder-decoder architecture for speedy TTS acoustic modelling, trained using optimal-transport conditional flow matching (OT-CFM). This yields an ODE-based decoder capable of high output quality in fewer synthesis steps than models trained using score matching. Careful design choices additionally ensure each synthesis step is fast to run. The method is probabilistic, non-autoregressive, and learns to speak from scratch without external alignments. Compared to strong pre-trained baseline models, the Matcha-TTS system has the smallest memory footprint, rivals the speed of the fastest model on long utterances, and attains the highest mean opinion score in a listening test.

Time Series Representation Learning (TSRL) focuses on generating informative representations for various Time Series (TS) modeling tasks. Traditional Self-Supervised Learning (SSL) methods in TSRL fall into four main categories: reconstructive, adversarial, contrastive, and predictive, each with a common challenge of sensitivity to noise and intricate data nuances. Recently, diffusion-based methods have shown advanced generative capabilities. However, they primarily target specific application scenarios like imputation and forecasting, leaving a gap in leveraging diffusion models for generic TSRL. Our work, Time Series Diffusion Embedding (TSDE), bridges this gap as the first diffusion-based SSL TSRL approach. TSDE segments TS data into observed and masked parts using an Imputation-Interpolation-Forecasting (IIF) mask. It applies a trainable embedding function, featuring dual-orthogonal Transformer encoders with a crossover mechanism, to the observed part. We train a reverse diffusion process conditioned on the embeddings, designed to predict noise added to the masked part. Extensive experiments demonstrate TSDE's superiority in imputation, interpolation, forecasting, anomaly detection, classification, and clustering. We also conduct an ablation study, present embedding visualizations, and compare inference speed, further substantiating TSDE's efficiency and validity in learning representations of TS data.

As text-to-speech technologies achieve remarkable naturalness in read-aloud tasks, there is growing interest in multimodal synthesis of verbal and non-verbal communicative behaviour, such as spontaneous speech and associated body gestures. This paper presents a novel, unified architecture for jointly synthesising speech acoustics and skeleton-based 3D gesture motion from text, trained using optimal-transport conditional flow matching (OT-CFM). The proposed architecture is simpler than the previous state of the art, has a smaller memory footprint, and can capture the joint distribution of speech and gestures, generating both modalities together in one single process. The new training regime, meanwhile, enables better synthesis quality in much fewer steps (network evaluations) than before. Uni- and multimodal subjective tests demonstrate improved speech naturalness, gesture human-likeness, and cross-modal appropriateness compared to existing benchmarks.

The goal of many sciences is to find causal relationships and understand underlying mechanisms. As the golden standard for finding causal relationships, doing randomized experiments can be difficult or impossible in some applications; hence, determining underlying causal relationships purely from observational data, i.e., causal discovery, has attracted more and more attention in many domains, such as earth science, biology, and healthcare. On the one hand, computational methods of causal discovery have been developed and improved significantly in the recent three decades. On the other hand, there are still many challenges in both practice and theory to further achieve real-world impacts. This thesis aims to introduce the typical methods and challenges of causal discovery and then elaborates on the contributions of the included papers that step forward to achieve more real-world impacts for causal discovery. It mainly covers four challenges: practical issues, understanding and generalizing the restrictive assumptions, the lack of benchmark data sets, and applications of causality in machine learning topics. Each included paper contributes to one of the challenges.

In the first paper, regarding causal discovery in the presence of missing data as one of the practical issues, we theoretically study the influence of missing values on causal discovery methods and then correct the errors in their results. Under mild assumptions, our proposed method provides asymptotically correct results.

In the second paper, we investigate the understanding of assumptions in a class of causal discovery methods. Such methods impose substantial constraints on functional classes and distributions of causal processes for determining causal relationships; however, the constraints are restrictive and there is a lack of good understanding. Therefore, we introduce a new dynamical-system view for understanding the methods and their constraints by connecting optimal transport and causal discovery. Furthermore, we provide a causal discovery criterion and a robust optimal transport-based algorithm. 

In the third paper, the evaluation of causal discovery methods is discussed. While it is too simplistic to evaluate causal discovery methods on synthetic data generated from random causal graphs, the real-world benchmark data sets with ground-truth causal relations are in great demand and always include practical issues. Thus, we create a neuropathic pain diagnosis simulator based on real-world patient records and domain knowledge. The simulator provides ground-truth causal relations and generates simulation data that cannot be distinguished by the medical expert. 

Finally, we explored an application of causality: Fairness in machine learning. Many fairness works are based on the constraints of static statistical measures across different demographic groups. It turns out that decisions under such constraints can lead to a pernicious long-term impact on the disadvantaged group. Therefore, we consider the underlying causal processes, theoretically analyze the equilibrium states of dynamical systems under various fairness constraints, show their impact on equilibrium states, and introduce potentially effective interventions to improve the equilibrium states. 

Målet för många vetenskapsområden är att hitta orsakssamband och förstå bakomliggande mekanismer. Som den gyllene standarden för att hitta orsakssamband kan slumpmässiga experiment vara svåra eller omöjliga i vissa tillämpningar; Därför har bestämning av underliggande orsakssamband enbart från observationsdata, d.v.s. kausal upptäckt, väckt mer och mer uppmärksamhet inom många områden, såsom geovetenskap, biologi och sjukvård. Å ena sidan har beräkningsmetoder för kausal upptäckt utvecklats och förbättrats avsevärt under de senaste tre decennierna. Å andra sidan finns det fortfarande många utmaningar kvar i både praktik och teori för att ytterligare uppnå verkliga effekter. Denna avhandling syftar till att introducera de typiska metoderna och utmaningarna för kausal upptäckt och sedan utveckla bidragen från de inkluderade artiklarna som tar kliv framåt för att uppnå fler verkliga effekter för kausal upptäckt. Den täcker huvudsakligen fyra utmaningar: praktiska frågor, förståelse och generalisering av de restriktiva antagandena, bristen på uppsättningar av referensdata och tillämpningar av kausalitet i maskininlärningsområden. Varje medföljande artikel bidrar till en av utmaningarna.

I den första artikeln, angående kausal upptäckt i närvaro av saknade data som en av de praktiska frågorna, studerar vi teoretiskt saknade värdens inverkan på metoder för kausal upptäckt och korrigerar sedan felen i deras resultat. Under milda antaganden ger vår föreslagna metod korrekta resultat.

I den andra artikeln undersöker vi förståelsen av antaganden i en klass av kausala upptäcktsmetoder. Sådana metoder lägger betydande begränsningar på funktionella klasser och fördelningar av kausala processer för att bestämma orsakssamband; dock är begränsningarna restriktiva och det saknas god förståelse. Därför introducerar vi en ny dynamisk systemvy för att förstå metoderna och deras begränsningar genom att koppla ihop optimal transport och kausal upptäckt. Dessutom tillhandahåller vi ett kausalt upptäcktskriterium och en robust optimal transport-baserad algoritm.

I den tredje artikeln diskuteras utvärderingen av kausala upptäcktsmetoder. Även om det är för förenklat att utvärdera kausala upptäcktsmetoder med syntetisk data genererad från slumpmässiga kausala grafer, så är uppsättningar av verklig referensdata med grund-sannings orsakssamband efterfrågade och inkluderar alltid praktiska frågor. Därför skapar vi en simulator för neuropatisk smärtdiagnos baserad på verkliga patientjournaler och domänkunskap. Simulatorn tillhandahåller sanna orsakssamband och genererar simuleringsdata som inte kan urskiljas av medicinska experter.

Slutligen undersökte vi en tillämpning av kausalitet: Rättvisa i maskininlärning. Många arbeten inom rättvisa är baserade på begränsningar av statiska statistiska mått över olika demografiska grupper. Det visar sig att beslut under sådana begränsningar kan leda till en skadlig långsiktig påverkan på den missgynnade gruppen. Därför tar vi hänsyn till de bakomliggande orsaksprocesserna, analyserar teoretiskt jämviktstillstånden i dynamiska system under olika rättvisa begränsningar, visar deras inverkan på jämviktstillstånd och introducerar potentiellt effektiva interventioner för att förbättra jämviktstillstånden.

Data-driven and controllable human motion synthesis and prediction are active research areas with various applications in interactive media and social robotics. Challenges remain in these fields for generating diverse motions given past observations and dealing with imperfect poses. This paper introduces MoDiff, an autoregressive probabilistic diffusion model over motion sequences conditioned on control contexts of other modalities. Our model integrates a cross-modal Transformer encoder and a Transformer-based decoder, which are found effective in capturing temporal correlations in motion and control modalities. We also introduce a new data dropout method based on the diffusion forward process to provide richer data representations and robust generation. We demonstrate the superior performance of MoDiff in controllable motion synthesis for locomotion with respect to two baselines and show the benefits of diffusion data dropout for robust synthesis and reconstruction of high-fidelity motion close to recorded data.

To determine causal relationships between two variables, approaches based on Functional Causal Models (FCMs) have been proposed by properly restricting model classes; however, the performance is sensitive to the model assumptions, which makes it difficult to use. In this paper, we provide a novel dynamical-system view of FCMs and propose a new framework for identifying causal direction in the bivariate case. We first show the connection between FCMs and optimal transport, and then study optimal transport under the constraints of FCMs. Furthermore, by exploiting the dynamical interpretation of optimal transport under the FCM constraints, we determine the corresponding underlying dynamical process of the static cause-effect pair data. It provides a new dimension for describing static causal discovery tasks while enjoying more freedom for modeling the quantitative causal influences. In particular, we show that Additive Noise Models (ANMs) correspond to volume-preserving pressure less flows. Consequently, based on their velocity field divergence, we introduce a criterion for determining causal direction. With this criterion, we propose a novel optimal transport-based algorithm for ANMs which is robust to the choice of models and extend it to post-nonlinear models. Our method demonstrated state-of-the-art results on both synthetic and causal discovery benchmark datasets.

Missing data are ubiquitous in many domains such as healthcare. When these data entries are not missing completely at random, the (conditional) independence relations in the observed data may be different from those in the complete data generated by the underlying causal process. Consequently, simply applying existing causal discovery methods to the observed data may lead to wrong conclusions. In this paper, we aim at developing a causal discovery method to recover the underlying causal structure from observed data that are missing under different mechanisms, including missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR). With missingness mechanisms represented by missingness graphs (m-graphs), we analyze conditions under which additional correction is needed to derive conditional independence/dependence relations in the complete data. Based on our analysis, we propose Missing Value PC (MVPC), which extends the PC algorithm to incorporate additional corrections. Our proposed MVPC is shown in theory to give asymptotically correct results even on data that are MAR or MNAR. Experimental results on both synthetic data and real healthcare applications illustrate that the proposed algorithm is able to find correct causal relations even in the general case of MNAR.

Although many fairness criteria have been proposed for decision making,  their long-term impact on the well-being of a population remains unclear. In this work, we study the dynamics of population qualification and algorithmic decisions under a partially observed decision making setting. By characterizing the equilibrium of such dynamics, we theoretically analyze the long-term impact of static fairness constraints on the equality and improvement of group well-being. Our results show that static fairness constraints can either promote the equality or exacerbate the disparity depending on the driven factor of qualification transitions and the effect of sensitive attributes on feature distributions. In turn, we consider possible effective interventions that improve group qualification or promote the equality of group qualification. Our theoretical results and experiments on static real-world datasets with simulated dynamics show the consistent findings with social science studies. 

Missing data are ubiquitous in many domains such as healthcare. When these data entries are not missing completely at random, the (condi-tional) independence relations in the observed data may be different from those in the complete data generated by the underlying causal process. Consequently, simply applying existing causal discovery methods to the observed data may lead to wrong conclusions. In this paper, we aim at de-veloping a causal discovery method to recover the underlying causal structure from observed data that are missing under different mechanisms, in-cluding missing completely at random (MCAR), missing at random (MAR), and missing hot at random (MNAR). With missingness mechanisms represented by missingness graphs (m-graphs), we analyze conditions under which additional correction is needed to derive conditional inde-pendence/dependence relations in the complete data. Based on our analysis, we propose Miss-ing Value PC (MVPC), which extends the PC algorithm to incorporate additional corrections. Our proposed MVPC is shown in theory to give asymptotically correct results even on data that are MAR or MNAR. Experimental results on both synthetic data and real healthcare applications il-lustrate that the proposed algorithm is able to find correct causal relations even in the general case of MNAR.