Efficient probability density estimation is a core challenge in statistical machine learning. Tensor-based probabilistic graph methods address interpretability and stability concerns encountered in neural network approaches. However, a substantial number of potential tensor permutations can lead to a tensor network with the same structure but varying expressive capabilities. In this paper, we take tensor ring decomposition for density estimator, which significantly reduces the number of permutation candidates while enhancing expressive capability compared with existing used decompositions. Additionally, a mixture model that incorporates multiple permutation candidates with adaptive weights is further designed, resulting in increased expressive flexibility and comprehensiveness. Different from the prevailing directions of tensor network structure/permutation search, our approach provides a new viewpoint inspired by ensemble learning. This approach acknowledges that suboptimal permutations can offer distinctive information besides that of optimal permutations. Experiments show the superiority of the proposed approach in estimating probability density for moderately dimensional datasets and sampling to capture intricate details.

Although Gaussian processes (GPs) with deep kernels have been successfully used for meta-learning in regression tasks, its uncertainty estimation performance can be poor. We propose a meta-learning method for calibrating deep kernel GPs for improving regression uncertainty estimation performance with a limited number of training data. The proposed method meta-learns how to calibrate uncertainty using data from various tasks by minimizing the test expected calibration error, and uses the knowledge for unseen tasks. We design our model such that the adaptation and calibration for each task can be performed without iterative procedures, which enables effective meta-learning. In particular, a task-specific uncalibrated output distribution is modeled by a GP with a task-shared encoder network, and it is transformed to a calibrated one using a cumulative density function of a task-specific Gaussian mixture model (GMM). By integrating the GP and GMM into our neural network-based model, we can meta-learn model parameters in an end-to-end fashion. Our experiments demonstrate that the proposed method improves uncertainty estimation performance while keeping high regression performance compared with the existing methods using real-world datasets in few-shot settings.

We present the first optimal rates for infinite-dimensional vector-valued ridge regression on a continuous scale of norms that interpolate between $L_2$ and the hypothesis space, which we consider as a vector-valued reproducing kernel Hilbert space. These rates allow to treat the misspecified case in which the true regression function is not contained in the hypothesis space. We combine standard assumptions on the capacity of the hypothesis space with a novel tensor product construction of vector-valued interpolation spaces in order to characterize the smoothness of the regression function. Our upper bound not only attains the same rate as real-valued kernel ridge regression, but also removes the assumption that the target regression function is bounded. For the lower bound, we reduce the problem to the scalar setting using a projection argument. We show that these rates are optimal in most cases and independent of the dimension of the output space. We illustrate our results for the special case of vector-valued Sobolev spaces.

Leveraging machine-learning methods to predict outcomes on some unlabeled datasets and then using these pseudo-outcomes in subsequent statistical inference is common in modern data analysis. Inference in this setting is often called post-prediction inference. We propose a novel, assumption-lean framework for inference under post-prediction setting, called \emph{Prediction De-Correlated inference} (PDC). Our approach can automatically adapt to any black-box machine-learning model and consistently outperforms supervised methods. The PDC framework also offers easy extensibility for accommodating multiple predictive models. Both numerical results and real-world data analysis support our theoretical results.

Score matching is an approach to learning probability distributions parametrized up to a constant of proportionality (e.g. Energy-Based Models). The idea is to fit the score of the distribution, rather than the likelihood, thus avoiding the need to evaluate the constant of proportionality. While there's a clear algorithmic benefit, the statistical "cost'' can be steep: recent work by Koehler et al. 2022 showed that for distributions that have poor isoperimetric properties (a large Poincar\'e or log-Sobolev constant), score matching is substantially statistically less efficient than maximum likelihood. However, many natural realistic distributions, e.g. multimodal distributions as simple as a mixture of two Gaussians in one dimension -- have a poor Poincar\'e constant. In this paper, we show a close connection between the mixing time of a broad class of Markov processes with generator $\mathcal{L}$ and an appropriately chosen generalized score matching loss that tries to fit $\frac{\mathcal{O} p}{p}$. This allows us to adapt techniques to speed up Markov chains to construct better score-matching losses. In particular, ``preconditioning'' the diffusion can be translated to an appropriate ``preconditioning'' of the score loss. Lifting the chain by adding a temperature like in simulated tempering can be shown to result in a Gaussian-convolution annealed score matching loss, similar to Song and Ermon, 2019. Moreover, we show that if the distribution being learned is a finite mixture of Gaussians in $d$ dimensions with a shared covariance, the sample complexity of annealed score matching is polynomial in the ambient dimension, the diameter of the means, and the smallest and largest eigenvalues of the covariance -- obviating the Poincar\'e constant-based lower bounds of the basic score matching loss shown in Koehler et al. 2022.

This dissertation will combine new tools and methodologies to answer pressing questions regarding inundation area and hurricane events in complex, heterogeneous changing environments. In addition to remote sensing approaches, citizen science and machine learning are both emerging fields that harness advancing technology to answer environmental management and disaster response questions. Freshwater lakes supply a large amount of inland water resources to sustain local and regional developments. However, some lake systems depend upon great fluctuation in water surface area.

We argue that time series analysis is fundamentally different in nature to either vision or natural language processing with respect to the forms of meaningful self-supervised learning tasks that can be defined. Motivated by this insight, we introduce a novel approach called \textit{Series2Vec} for self-supervised representation learning. Unlike other self-supervised methods in time series, which carry the risk of positive sample variants being less similar to the anchor sample than series in the negative set, Series2Vec is trained to predict the similarity between two series in both temporal and spectral domains through a self-supervised task. Series2Vec relies primarily on the consistency of the unsupervised similarity step, rather than the intrinsic quality of the similarity measurement, without the need for hand-crafted data augmentation. To further enforce the network to learn similar representations for similar time series, we propose a novel approach that applies order-invariant attention to each representation within the batch during training. Our evaluation of Series2Vec on nine large real-world datasets, along with the UCR/UEA archive, shows enhanced performance compared to current state-of-the-art self-supervised techniques for time series. Additionally, our extensive experiments show that Series2Vec performs comparably with fully supervised training and offers high efficiency in datasets with limited-labeled data. Finally, we show that the fusion of Series2Vec with other representation learning models leads to enhanced performance for time series classification. Code and models are open-source at \url{https://github.com/Navidfoumani/Series2Vec.}

The rapid development of automated driving systems in recent years has led to improvements in road safety and travel comfort. One typical function of these systems is Lane Keep Assist, which generally does not take human driving preferences into account. In our previous work, we have demonstrated that it is possible to implement a Lane Keep Assist function that is appropriate to human preferences using a trajectory planning algorithm based on a linear driving model. In our current work, we investigated how to separate the driving styles of individual drivers. We assumed that there are three driving styles: sporty, neutral and defensive. To prove these relations, clustering methods were applied to previously recorded measurements . Simulations with parameters describing the average behaviour of the classes (re-simulated with clustered types) showed that the resulting paths successfully classified drivers, that the 3 classes are distinct in their behaviour and that our model reproduces these behaviours.

E-Commerce (EC) websites provide a large amount of useful information that exceed human cognitive processing ability. In order to help customers in comparing alternatives when buying a product, previous studies designed opinion summarization systems based on customer reviews. They ignored templates' information provided by manufacturers, although these descriptive information have much product aspects or characteristics. Therefore, this paper proposes a methodology coined as SEOpinion (Summa-rization and Exploration of Opinions) which provides a summary for the product aspects and spots opinion(s) regarding them, using a combination of templates' information with the customer reviews in two main phases. First, the Hierarchical Aspect Extraction (HAE) phase creates a hierarchy of product aspects from the template. Subsequently, the Hierarchical Aspect-based Opinion Summarization (HAOS) phase enriches this hierarchy with customers' opinions; to be shown to other potential buyers. To test the feasibility of using Deep Learning-based BERT techniques with our approach, we have created a corpus by gathering information from the top five EC websites for laptops. The experimental results show that Recurrent Neural Network (RNN) achieves better results (77.4% and 82.6% in terms of F1-measure for the first and second phase) than the Convolutional Neural Network (CNN) and the Support Vector Machine (SVM) technique.

This research report presents a proof-of-concept study on the application of machine learning techniques to video and speech data collected during diagnostic cognitive assessments of children with a neurodevelopmental disorder. The study utilised a dataset of 39 video recordings, capturing extensive sessions where clinicians administered, among other things, four cognitive assessment tests. From the first 40 minutes of each clinical session, covering the administration of the Wechsler Intelligence Scale for Children (WISC-V), we extracted head positions and speech turns of both clinician and child. Despite the limited sample size and heterogeneous recording styles, the analysis successfully extracted path signatures as features from the recorded data, focusing on patient-clinician interactions. Importantly, these features quantify the interpersonal dynamics of the assessment process (dialogue and movement patterns). Results suggest that these features exhibit promising potential for predicting all cognitive tests scores of the entire session length and for prototyping a predictive model as a clinical decision support tool. Overall, this proof of concept demonstrates the feasibility of leveraging machine learning techniques for clinical video and speech data analysis in order to potentially enhance the efficiency of cognitive assessments for neurodevelopmental disorders in children.