Understanding how biomarker distributions evolve over time is a central challenge in digital health and chronic disease monitoring. In diabetes, changes in the distribution of glucose measurements can reveal patterns of disease progression and treatment response that conventional summary measures miss. Motivated by a 26-week clinical trial comparing the closed-loop insulin delivery system t:slim X2 with standard therapy in children with type 1 diabetes, we propose a probabilistic framework to model the continuous-time evolution of time-indexed distributions using continuous glucose monitoring data (CGM) collected every five minutes. We represent the glucose distribution as a Gaussian mixture, with time-varying mixture weights governed by a neural ODE. We estimate the model parameter using a distribution-matching criterion based on the maximum mean discrepancy. The resulting framework is interpretable, computationally efficient, and sensitive to subtle temporal distributional changes. Applied to CGM trial data, the method detects treatment-related improvements in glucose dynamics that are difficult to capture with traditional analytical approaches.

Medical researchers are coming to appreciate that many diseases are in fact complex, heterogeneous syndromes composed of subpopulations that express different variants of a related complication. Longitudinal data extracted from individual electronic health records (EHR) offer an exciting new way to study subtle differences in the way these diseases progress over time. In this paper, we focus on answering two questions that can be asked using these databases of longitudinal EHR data. First, we want to understand whether there are individuals with similar disease trajectories and whether there are a small number of degrees of freedom that account for differences in trajectories across the population. Second, we want to understand how important clinical outcomes are associated with disease trajectories. To answer these questions, we propose the Disease Trajectory Map (DTM), a novel probabilistic model that learns low-dimensional representations of sparse and irregularly sampled longitudinal data. We propose a stochastic variational inference algorithm for learning the DTM that allows the model to scale to large modern medical datasets. To demonstrate the DTM, we analyze data collected on patients with the complex autoimmune disease, scleroderma. We find that DTM learns meaningful representations of disease trajectories and that the representations are significantly associated with important clinical outcomes.

Nanopore sequencing is the third-generation sequencing technology with capabilities of generating long-read sequences and directly measuring modifications on DNA/RNA molecules, which makes it ideal for biological applications such as human Telomere-to-Telomere (T2T) genome assembly, Ebola virus surveillance and COVID-19 mRNA vaccine development. However, accuracies of computational methods in various tasks of Nanopore sequencing data analysis are far from satisfactory. For instance, the base calling accuracy of Nanopore RNA sequencing is $\sim$90\%, while the aim is $\sim$99.9\%. This highlights an urgent need of contributions from the machine learning community. A bottleneck that prevents machine learning researchers from entering this field is the lack of a large integrated benchmark dataset.

While synthetic data hold great promise for privacy protection, their statistical analysis poses significant challenges that necessitate innovative solutions. The use of deep generative models (DGMs) for synthetic data generation is known to induce considerable bias and imprecision into synthetic data analyses, compromising their inferential utility as opposed to original data analyses. This bias and uncertainty can be substantial enough to impede statistical convergence rates, even in seemingly straightforward analyses like mean calculation.

Data analysis is a crucial analytical process essential for deriving insights from real-world databases.

However, differential privacy's worst-case nature entails scaling such noise to the range of the queries even for

However,in manyapplications there are several different parameters one might wish to vary: for example, scale and density. In contrast to the one-parameter setting, techniques for applying statistics and machine learning in the setting of multiparameter persistence are not well understood due to the lack of a concise representationoftheresults.

Now,since|N(v)|=β,itholds (Px)[v]= a+b 2, thus verifying the first claim of the lemma as the choice ofv was arbitrary. This construction essentially generalizes the graph demonstrated in Figure 1 of the main paper (see Sec. 7). The following lemma shows that onsuch graphs, the filter responses ofgθ for aconstant signal will encode some geometric information, butwill not distinguish between the cycles inthe graph. These responses with appropriate color coding give the illustration in Figure 1 in the main paper. Validation & testing procedure: All tests were done using train-validation-test splits of the datasets, where validation accuracy is used for tuning hyperparameters and test accuracy is reportedinthecomparisontable.