Single-cell multi-omics data contain huge information of cellular states, and analyzing these data can reveal valuable insights into cellular heterogeneity, diseases, and biological processes. However, as cell differentiation \& development is a continuous and dynamic process, it remains challenging to computationally model and infer cell interaction patterns based on single-cell multi-omics data. This paper presents scI2CL, a new single-cell multi-omics fusion framework based on intra- and inter-omics contrastive learning, to learn comprehensive and discriminative cellular representations from complementary multi-omics data for various downstream tasks. Extensive experiments of four downstream tasks validate the effectiveness of scI2CL and its superiority over existing peers. Concretely, in cell clustering, scI2CL surpasses eight state-of-the-art methods on four widely-used real-world datasets. In cell subtyping, scI2CL effectively distinguishes three latent monocyte cell subpopulations, which are not discovered by existing methods. Simultaneously, scI2CL is the only method that correctly constructs the cell developmental trajectory from hematopoietic stem and progenitor cells to Memory B cells. In addition, scI2CL resolves the misclassification of cell types between two subpopulations of CD4+ T cells, while existing methods fail to precisely distinguish the mixed cells. In summary, scI2CL can accurately characterize cross-omics relationships among cells, thus effectively fuses multi-omics data and learns discriminative cellular representations to support various downstream analysis tasks.

Background: Existing robust, pervasive device-based systems developed in recent years to detect depression require data collected over a long period and may not be effective in cases where early detection is crucial. Objective: Our main objective was to develop a minimalistic system to identify depression using data retrieved in the fastest possible time. Methods: We developed a fast tool that retrieves the past 7 days' app usage data in 1 second (mean 0.31, SD 1.10 seconds). A total of 100 students from Bangladesh participated in our study, and our tool collected their app usage data. To identify depressed and nondepressed students, we developed a diverse set of ML models. We selected important features using the stable approach, along with 3 main types of feature selection (FS) approaches. Results: Leveraging only the app usage data retrieved in 1 second, our light gradient boosting machine model used the important features selected by the stable FS approach and correctly identified 82.4% (n=42) of depressed students (precision=75%, F1-score=78.5%). Moreover, after comprehensive exploration, we presented a parsimonious stacking model where around 5 features selected by the all-relevant FS approach Boruta were used in each iteration of validation and showed a maximum precision of 77.4% (balanced accuracy=77.9%). A SHAP analysis of our best models presented behavioral markers that were related to depression. Conclusions: Due to our system's fast and minimalistic nature, it may make a worthwhile contribution to identifying depression in underdeveloped and developing regions. In addition, our detailed discussion about the implication of our findings can facilitate the development of less resource-intensive systems to better understand students who are depressed.

Accurate air quality prediction is becoming increasingly important in the environmental field. To address issues such as low prediction accuracy and slow real-time updates in existing models, which lead to lagging prediction results, we propose a Transformer-based spatiotemporal data prediction method (Ada-TransGNN) that integrates global spatial semantics and temporal behavior. The model constructs an efficient and collaborative spatiotemporal block set comprising a multi-head attention mechanism and a graph convolutional network to extract dynamically changing spatiotemporal dependency features from complex air quality monitoring data. Considering the interaction relationships between different monitoring points, we propose an adaptive graph structure learning module, which combines spatiotemporal dependency features in a data-driven manner to learn the optimal graph structure, thereby more accurately capturing the spatial relationships between monitoring points. Additionally, we design an auxiliary task learning module that enhances the decoding capability of temporal relationships by integrating spatial context information into the optimal graph structure representation, effectively improving the accuracy of prediction results. We conducted comprehensive evaluations on a benchmark dataset and a novel dataset (Mete-air). The results demonstrate that our model outperforms existing state-of-the-art prediction models in short-term and long-term predictions.

Modern computer vision models have proven to be highly useful for medical imaging classification and segmentation tasks, but the scarcity of medical imaging data often limits the efficacy of models trained from scratch. Transfer learning has emerged as a pivotal solution to this, enabling the fine-tuning of high-performance models on small data. Mei et al. (2022) found that pre-training CNNs on a large dataset of radiologist-labeled images (RadImageNet) enhanced model performance on downstream tasks compared to ImageNet pretraining. The present work extends Mei et al. (2022) by conducting a comprehensive investigation to determine optimal CNN architectures for breast lesion malignancy detection and ACL tear detection, as well as performing statistical analysis to compare the effect of RadImageNet and ImageNet pre-training on downstream model performance. Our findings suggest that 1-dimensional convolutional classifiers with skip connections, ResNet50 pre-trained backbones, and partial backbone unfreezing yields optimal downstream medical classification performance. Our best models achieve AUCs of 0.9969 for ACL tear detection and 0.9641 for breast nodule malignancy detection, competitive with the results reported by Mei et al. (2022) and surpassing other previous works. We do not find evidence confirming RadImageNet pre-training to provide superior downstream performance for ACL tear and breast lesion classification tasks.

Langevin algorithms are popular Markov chain Monte Carlo (MCMC) methods for large-scale sampling problems that often arise in data science. We propose Monte Carlo algorithms based on the discretizations of $P$-th order Langevin dynamics for any $P\geq 3$. Our design of $P$-th order Langevin Monte Carlo (LMC) algorithms is by combining splitting and accurate integration methods. We obtain Wasserstein convergence guarantees for sampling from distributions with log-concave and smooth densities. Specifically, the mixing time of the $P$-th order LMC algorithm scales as $O\left(d^{\frac{1}{R}}/ε^{\frac{1}{2R}}\right)$ for $R=4\cdot 1_{\{ P=3\}}+ (2P-1)\cdot 1_{\{ P\geq 4\}}$, which has a better dependence on the dimension $d$ and the accuracy level $ε$ as $P$ grows. Numerical experiments illustrate the efficiency of our proposed algorithms.

In this PhD thesis, we propose a novel framework for uncertainty quantification in machine learning, which is based on proper scores. Uncertainty quantification is an important cornerstone for trustworthy and reliable machine learning applications in practice. Usually, approaches to uncertainty quantification are problem-specific, and solutions and insights cannot be readily transferred from one task to another. Proper scores are loss functions minimized by predicting the target distribution. Due to their very general definition, proper scores apply to regression, classification, or even generative modeling tasks. We contribute several theoretical results, that connect epistemic uncertainty, aleatoric uncertainty, and model calibration with proper scores, resulting in a general and widely applicable framework. We achieve this by introducing a general bias-variance decomposition for strictly proper scores via functional Bregman divergences. Specifically, we use the kernel score, a kernel-based proper score, for evaluating sample-based generative models in various domains, like image, audio, and natural language generation. This includes a novel approach for uncertainty estimation of large language models, which outperforms state-of-the-art baselines. Further, we generalize the calibration-sharpness decomposition beyond classification, which motivates the definition of proper calibration errors. We then introduce a novel estimator for proper calibration errors in classification, and a novel risk-based approach to compare different estimators for squared calibration errors. Last, we offer a decomposition of the kernel spherical score, another kernel-based proper score, allowing a more fine-grained and interpretable evaluation of generative image models.

High-dimensional Bayesian Optimization (BO) has attracted significant attention in recent research. However, existing methods have mainly focused on optimizing in continuous domains, while combinatorial (ordinal and categorical) and mixed domains still remain challenging. In this paper, we first propose MOCA-HESP, a novel high-dimensional BO method for combinatorial and mixed variables. The key idea is to leverage the hyper-ellipsoid space partitioning (HESP) technique with different categorical encoders to work with high-dimensional, combinatorial and mixed spaces, while adaptively selecting the optimal encoders for HESP using a multi-armed bandit technique. Our method, MOCA-HESP, is designed as a \textit{meta-algorithm} such that it can incorporate other combinatorial and mixed BO optimizers to further enhance the optimizers' performance. Finally, we develop three practical BO methods by integrating MOCA-HESP with state-of-the-art BO optimizers for combinatorial and mixed variables: standard BO, CASMOPOLITAN, and Bounce. Our experimental results on various synthetic and real-world benchmarks show that our methods outperform existing baselines. Our code implementation can be found at https://github.com/LamNgo1/moca-hesp

We develop a novel optimistic gradient-type algorithmic framework, combining both Nesterov's acceleration and variance-reduction techniques, to solve a class of generalized equations involving possibly nonmonotone operators in data-driven applications. Our framework covers a wide class of stochastic variance-reduced schemes, including mini-batching, and control variate unbiased and biased estimators. We establish that our method achieves $\mathcal{O}(1/k^2)$ convergence rates in expectation on the squared norm of residual under the Lipschitz continuity and a ``co-hypomonotonicity-type'' assumptions, improving upon non-accelerated counterparts by a factor of $1/k$. We also prove faster $o(1/k^2)$ convergence rates, both in expectation and almost surely. In addition, we show that the sequence of iterates of our method almost surely converges to a solution of the underlying problem. We demonstrate the applicability of our method using general error bound criteria, covering mini-batch stochastic estimators as well as three well-known control variate estimators: loopless SVRG, SAGA, and loopless SARAH, for which the last three variants attain significantly better oracle complexity compared to existing methods. We validate our framework and theoretical results through two numerical examples. The preliminary results illustrate promising performance of our accelerated method over its non-accelerated counterparts.

In safety-critical applications data-driven models must not only be accurate but also provide reliable uncertainty estimates. This property, commonly referred to as calibration, is essential for risk-aware decision-making. In regression a wide variety of calibration metrics and recalibration methods have emerged. However, these metrics differ significantly in their definitions, assumptions and scales, making it difficult to interpret and compare results across studies. Moreover, most recalibration methods have been evaluated using only a small subset of metrics, leaving it unclear whether improvements generalize across different notions of calibration. In this work, we systematically extract and categorize regression calibration metrics from the literature and benchmark these metrics independently of specific modelling methods or recalibration approaches. Through controlled experiments with real-world, synthetic and artificially miscalibrated data, we demonstrate that calibration metrics frequently produce conflicting results. Our analysis reveals substantial inconsistencies: many metrics disagree in their evaluation of the same recalibration result, and some even indicate contradictory conclusions. This inconsistency is particularly concerning as it potentially allows cherry-picking of metrics to create misleading impressions of success. We identify the Expected Normalized Calibration Error (ENCE) and the Coverage Width-based Criterion (CWC) as the most dependable metrics in our tests. Our findings highlight the critical role of metric selection in calibration research.

When do diffusion models reproduce their training data, and when are they able to generate samples beyond it? A practically relevant theoretical understanding of this interplay between memorization and generalization may significantly impact real-world deployments of diffusion models with respect to issues such as copyright infringement and data privacy. In this work, to disentangle the different factors that influence memorization and generalization in practical diffusion models, we introduce a scientific and mathematical "laboratory" for investigating these phenomena in diffusion models trained on fully synthetic or natural image-like structured data. Within this setting, we hypothesize that the memorization or generalization behavior of an underparameterized trained model is determined by the difference in training loss between an associated memorizing model and a generalizing model. To probe this hypothesis, we theoretically characterize a crossover point wherein the weighted training loss of a fully generalizing model becomes greater than that of an underparameterized memorizing model at a critical value of model (under)parameterization. We then demonstrate via carefully-designed experiments that the location of this crossover predicts a phase transition in diffusion models trained via gradient descent, validating our hypothesis. Ultimately, our theory enables us to analytically predict the model size at which memorization becomes predominant. Our work provides an analytically tractable and practically meaningful setting for future theoretical and empirical investigations. Code for our experiments is available at https://github.com/DruvPai/diffusion_mem_gen.