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In many applications, geodesic hierarchical models are adequate for the study of temporal observations. We employ such a model derived for manifold-valued data to Kendall's shape space. In particular, instead of the Sasaki metric, we adapt a functional-based metric, which increases the computational efficiency and does not require the implementation of the curvature tensor. We propose the corresponding variational time discretization of geodesics and employ the approach for longitudinal analysis of 2D rat skulls shapes as well as 3D shapes derived from an imaging study on osteoarthritis. Particularly, we perform hypothesis test and estimate the mean trends.

Inspired by ideas from optimal transport theory we present Trust the Critics (TTC), a new algorithm for generative modelling. This algorithm eliminates the trainable generator from a Wasserstein GAN; instead, it iteratively modifies the source data using gradient descent on a sequence of trained critic networks. This is motivated in part by the misalignment which we observed between the optimal transport directions provided by the gradients of the critic and the directions in which data points actually move when parametrized by a trainable generator. Previous work has arrived at similar ideas from different viewpoints, but our basis in optimal transport theory motivates the choice of an adaptive step size which greatly accelerates convergence compared to a constant step size. Using this step size rule, we prove an initial geometric convergence rate in the case of source distributions with densities. These convergence rates cease to apply only when a non-negligible set of generated data is essentially indistinguishable from real data. Resolving the misalignment issue improves performance, which we demonstrate in experiments that show that given a fixed number of training epochs, TTC produces higher quality images than a comparable WGAN, albeit at increased memory requirements. In addition, TTC provides an iterative formula for the transformed density, which traditional WGANs do not. Finally, TTC can be applied to map any source distribution onto any target; we demonstrate through experiments that TTC can obtain competitive performance in image generation, translation, and denoising without dedicated algorithms.

Precision medicine is a clinical approach for disease prevention, detection and treatment, which considers each individual's genetic background, environment and lifestyle. The development of this tailored avenue has been driven by the increased availability of omics methods, large cohorts of temporal samples, and their integration with clinical data. Despite the immense progression, existing computational methods for data analysis fail to provide appropriate solutions for this complex, high-dimensional and longitudinal data. In this work we have developed a new method termed TCAM, a dimensionality reduction technique for multi-way data, that overcomes major limitations when doing trajectory analysis of longitudinal omics data. Using real-world data, we show that TCAM outperforms traditional methods, as well as state-of-the-art tensor-based approaches for longitudinal microbiome data analysis. Moreover, we demonstrate the versatility of TCAM by applying it to several different omics datasets, and the applicability of it as a drop-in replacement within straightforward ML tasks.

We introduce Gaussian orthogonal latent factor processes for modeling and predicting large correlated data. To handle the computational challenge, we first decompose the likelihood function of the Gaussian random field with a multi-dimensional input domain into a product of densities at the orthogonal components with lower-dimensional inputs. The continuous-time Kalman filter is implemented to compute the likelihood function efficiently without making approximations. We also show that the posterior distribution of the factor processes is independent, as a consequence of prior independence of factor processes and orthogonal factor loading matrix. For studies with large sample sizes, we propose a flexible way to model the mean, and we derive the marginal posterior distribution to solve identifiability issues in sampling these parameters. Both simulated and real data applications confirm the outstanding performance of this method.

This work deals with the analysis of longitudinal ordinal responses. The novelty of the proposed approach is in modeling simultaneously the temporal dynamics of a latent trait of interest, measured via the observed ordinal responses, and the answering behaviors influenced by response styles, through hidden Markov models (HMMs) with two latent components. This approach enables the modeling of (i) the substantive latent trait, controlling for response styles; (ii) the change over time of latent trait and answering behavior, allowing also dependence on individual characteristics. For the proposed HMMs, estimation procedures, methods for standard errors calculation, measures of goodness of fit and classification, and full-conditional residuals are discussed. The proposed model is fitted to ordinal longitudinal data from the Survey on Household Income and Wealth (Bank of Italy) to give insights on the evolution of the Italian households financial capability.

Semiconductor device models are essential to understand the charge transport in thin film transistors (TFTs). Using these TFT models to draw inference involves estimating parameters used to fit to the experimental data. These experimental data can involve extracted charge carrier mobility or measured current. Estimating these parameters help us draw inferences about device performance. Fitting a TFT model for a given experimental data using the model parameters relies on manual fine tuning of multiple parameters by human experts. Several of these parameters may have confounding effects on the experimental data, making their individual effect extraction a non-intuitive process during manual tuning. To avoid this convoluted process, we propose a new method for automating the model parameter extraction process resulting in an accurate model fitting. In this work, model choice based approximate Bayesian computation (aBc) is used for generating the posterior distribution of the estimated parameters using observed mobility at various gate voltage values. Furthermore, it is shown that the extracted parameters can be accurately predicted from the mobility curves using gradient boosted trees. This work also provides a comparative analysis of the proposed framework with fine-tuned neural networks wherein the proposed framework is shown to perform better.

Score-based generative models and diffusion probabilistic models have been successful at generating high-quality samples in continuous domains such as images and audio. However, due to their Langevin-inspired sampling mechanisms, their application to discrete and sequential data has been limited. In this work, we present a technique for training diffusion models on sequential data by parameterizing the discrete domain in the continuous latent space of a pre-trained variational autoencoder. Our method is non-autoregressive and learns to generate sequences of latent embeddings through the reverse process and offers parallel generation with a constant number of iterative refinement steps. We apply this technique to modeling symbolic music and show strong unconditional generation and post-hoc conditional infilling results compared to autoregressive language models operating over the same continuous embeddings.

This paper presents a novel Subject-dependent Deep Aging Path (SDAP), which inherits the merits of both Generative Probabilistic Modeling and Inverse Reinforcement Learning to model the facial structures and the longitudinal face aging process of a given subject. The proposed SDAP is optimized using tractable log-likelihood objective functions with Convolutional Neural Networks (CNNs) based deep feature extraction. Instead of applying a fixed aging development path for all input faces and subjects, SDAP is able to provide the most appropriate aging development path for individual subject that optimizes the reward aging formulation. Unlike previous methods that can take only one image as the input, SDAP further allows multiple images as inputs, i.e. all information of a subject at either the same or different ages, to produce the optimal aging path for the given subject. Finally, SDAP allows efficiently synthesizing in-the-wild aging faces. The proposed model is experimented in both tasks of face aging synthesis and cross-age face verification. The experimental results consistently show SDAP achieves the state-of-the-art performance on numerous face aging databases, i.e. FG-NET, MORPH, AginG Faces in the Wild (AGFW), and Cross-Age Celebrity Dataset (CACD). Furthermore, we also evaluate the performance of SDAP on large-scale Megaface challenge to demonstrate the advantages of the proposed solution.

Dynamic topic models (DTMs) model the evolution of prevalent themes in literature, online media, and other forms of text over time. DTMs assume that word co-occurrence statistics change continuously and therefore impose continuous stochastic process priors on their model parameters. These dynamical priors make inference much harder than in regular topic models, and also limit scalability. In this paper, we present several new results around DTMs. First, we extend the class of tractable priors from Wiener processes to the generic class of Gaussian processes (GPs). This allows us to explore topics that develop smoothly over time, that have a long-term memory or are temporally concentrated (for event detection). Second, we show how to perform scalable approximate inference in these models based on ideas around stochastic variational inference and sparse Gaussian processes. This way we can train a rich family of DTMs to massive data. Our experiments on several large-scale datasets show that our generalized model allows us to find interesting patterns that were not accessible by previous approaches.