In the context of cardiovascular diseases (CVD) that exhibit an elevated prevalence and mortality, the electrocardiogram (ECG) is a popular and standard diagnostic tool for doctors, commonly utilizing a 12-lead configuration in clinical practice. However, the 10 electrodes placed on the surface would cause a lot of inconvenience and discomfort, while the rapidly advancing wearable devices adopt the reduced-lead or single-lead ECG to reduce discomfort as a solution in long-term monitoring. Since the single-lead ECG is a subset of 12-lead ECG, it provides insufficient cardiac health information and plays a substandard role in real-world healthcare applications. Hence, it is necessary to utilize signal generation technologies to reduce their clinical importance gap by reconstructing 12-lead ECG from the real single-lead ECG. Specifically, this study proposes a multi-channel masked autoencoder (MCMA) for this goal. In the experimental results, the visualized results between the generated and real signals can demonstrate the effectiveness of the proposed framework. At the same time, this study introduces a comprehensive evaluation benchmark named ECGGenEval, encompassing the signal-level, feature-level, and diagnostic-level evaluations, providing a holistic assessment of 12-lead ECG signals and generative model. Further, the quantitative experimental results are as follows, the mean square errors of 0.0178 and 0.0658, correlation coefficients of 0.7698 and 0.7237 in the signal-level evaluation, the average F1-score with two generated 12-lead ECG is 0.8319 and 0.7824 in the diagnostic-level evaluation, achieving the state-of-the-art performance. The open-source code is publicly available at \url{https://github.com/CHENJIAR3/MCMA}.

In this work, we address the challenge of reconstructing the complete 12-lead ECG signal from incomplete parts of it. We focus on two main scenarii: (i) reconstructing missing signal segments within an ECG lead and (ii) recovering missing leads from a single-lead. We propose a model with a U-Net architecture trained on a novel objective function to address the reconstruction problem. This function incorporates both spatial and temporal aspects of the ECG by combining the distance in amplitude between the reconstructed and real signals with the signal trend. Through comprehensive assessments using both a real-life dataset and a publicly accessible one, we demonstrate that the proposed approach consistently outperforms state-of-the-art methods based on generative adversarial networks and a CopyPaste strategy. Our proposed model demonstrates superior performance in standard distortion metrics and preserves critical ECG characteristics, particularly the P, Q, R, S, and T wave coordinates. Two emerging clinical applications emphasize the relevance of our work. The first is the increasing need to digitize paper-stored ECGs for utilization in AI-based applications (automatic annotation and risk-quantification), often limited to digital ECG complete 10s recordings. The second is the widespread use of wearable devices that record ECGs but typically capture only a small subset of the 12 standard leads. In both cases, a non-negligible amount of information is lost or not recorded, which our approach aims to recover to overcome these limitations.

Transfer Learning is an area of statistics and machine learning research that seeks answers to the following question: how do we build successful learning algorithms when the data available for training our model is qualitatively different from the data we hope the model will perform well on? In this thesis, we focus on a specific area of Transfer Learning called label shift, also known as quantification. In quantification, the aforementioned discrepancy is isolated to a shift in the distribution of the response variable. In such a setting, accurately inferring the response variable's new distribution is both an important estimation task in its own right and a crucial step for ensuring that the learning algorithm can adapt to the new data. We make two contributions to this field. First, we present a new procedure called SELSE which estimates the shift in the response variable's distribution. Second, we prove that SELSE is semiparametric efficient among a large family of quantification algorithms, i.e., SELSE's normalized error has the smallest possible asymptotic variance matrix compared to any other algorithm in that family. This family includes nearly all existing algorithms, including ACC/PACC quantifiers and maximum likelihood based quantifiers such as EMQ and MLLS. Empirical experiments reveal that SELSE is competitive with, and in many cases outperforms, existing state-of-the-art quantification methods, and that this improvement is especially large when the number of test samples is far greater than the number of train samples.

Contagions such as the spread of popular news stories, or infectious diseases, propagate in cascades over dynamic networks with unobservable topologies. However, "social signals" such as product purchase time, or blog entry timestamps are measurable, and implicitly depend on the underlying topology, making it possible to track it over time. Interestingly, network topologies often "jump" between discrete states that may account for sudden changes in the observed signals. The present paper advocates a switched dynamic structural equation model to capture the topology-dependent cascade evolution, as well as the discrete states driving the underlying topologies. Conditions under which the proposed switched model is identifiable are established. Leveraging the edge sparsity inherent to social networks, a recursive $\ell_1$-norm regularized least-squares estimator is put forth to jointly track the states and network topologies. An efficient first-order proximal-gradient algorithm is developed to solve the resulting optimization problem. Numerical experiments on both synthetic data and real cascades measured over the span of one year are conducted, and test results corroborate the efficacy of the advocated approach.

We study the notion of informedness in a client-consultant setting. Using a software simulator, we examine the extent to which it pays off for consultants to provide their clients with advice that is well-informed, or with advice that is merely meant to appear to be well-informed. The latter strategy is beneficial in that it costs less resources to keep up-to-date, but carries the risk of a decreased reputation if the clients discover the low level of informedness of the consultant. Our experimental results indicate that under different circumstances, different strategies yield the optimal results (net profit) for the consultants.