A new SVD approach to optimal topic estimation

In the probabilistic topic models, the quantity of interest---a low-rank matrix consisting of topic vectors---is hidden in the text corpus matrix, masked by noise, and Singular Value Decomposition (SVD) is a potentially useful tool for learning such a matrix. However, different rows and columns of the matrix are usually in very different scales and the connection between this matrix and the singular vectors of the text corpus matrix are usually complicated and hard to spell out, so how to use SVD for learning topic models faces challenges. We overcome the challenges by introducing a proper Pre-SVD normalization of the text corpus matrix and a proper column-wise scaling for the matrix of interest, and by revealing a surprising Post-SVD low-dimensional {\it simplex} structure. The simplex structure, together with the Pre-SVD normalization and column-wise scaling, allows us to conveniently reconstruct the matrix of interest, and motivates a new SVD-based approach to learning topic models. We show that under the popular probabilistic topic model \citep{hofmann1999}, our method has a faster rate of convergence than existing methods in a wide variety of cases. In particular, for cases where documents are long or $n$ is much larger than $p$, our method achieves the optimal rate. At the heart of the proofs is a tight element-wise bound on singular vectors of a multinomially distributed data matrix, which do not exist in literature and we have to derive by ourself. We have applied our method to two data sets, Associated Process (AP) and Statistics Literature Abstract (SLA), with encouraging results. In particular, there is a clear simplex structure associated with the SVD of the data matrices, which largely validates our discovery.Comment: 73 pages, 8 figures, 6 tables; considered two different VH algorithm, OVH and GVH, and provided theoretical analysis for each algorithm; re-organized upper bound theory part; added the subsection of comparing error rate with other existing methods; provided another improved version of error analysis through Bernstein inequality for martingale

Heart Rate Estimation During Physical Exercise Using Wrist-Type Ppg Sensors

Accurate heart rate monitoring during intense physical exercise is a challenging problem due to the high levels of motion artifacts (MA) in photoplethysmography (PPG) sensors. PPG is a non-invasive optical sensor that is being used in wearable devices to measure blood flow changes using the property of light reflection and absorption, allowing the extraction of vital signals such as the heart rate (HR). However, the sensor is susceptible to MA which increases during physical activity. This occurs since the frequency range of movement and HR overlaps, difficulting correct HR estimation. For this reason, MA removal has remained an active topic under research. Several approaches have been developed in the recent past and among these, a Kalman filter (KF) based approach showed promising results for an accurate estimation and tracking using PPG sensors. However, this previous tracker was demonstrated for a particular dataset, with manually tuned parameters. Moreover, such trackers do not account for the correct method for fusing data. Such a custom approach might not perform accurately in practical scenarios, where the amount of MA and the heart rate variability (HRV) depend on numerous, unpredictable factors. Thus, an approach to automatically tune the KF based on the Expectation-Maximization (EM) algorithm, with a measurement fusion approach is developed. The applicability of such a method is demonstrated using an open-source PPG database, as well as a developed synthetic generation tool that models PPG and accelerometer (ACC) signals during predetermined physical activities

High-fidelity simulation increases obstetric self-assurance and skills in undergraduate medical students

Objective: Teaching intrapartum care is one of the most challenging tasks in undergraduate medical education. High-fidelity obstetric simulators might support students' learning experience. The specific educational impact of these simulators compared with traditional methods of model-based obstetric teaching has not yet been determined. Study design: We randomly assigned 46 undergraduate medical students to be taught using either a high-fidelity simulator or a scale wood-and-leather phantom. Their self-assessments were evaluated using a validated questionnaire. We assessed obstetric skills and asked students to solve obstetric paper cases. Main outcome measures: Assessment of fidelity-specific teaching impact on procedural knowledge, motivation, and interest in obstetrics as well as obstetric skills using high- and low-fidelity training models. Results: High-fidelity simulation specifically improved students' feeling that they understood both the physiology of parturition and the obstetric procedures. Students in the simulation group also felt better prepared for obstetric house jobs and performed better in obstetric skills evaluations. However, the two groups made equivalent obstetric decisions. Conclusion: This study provides first data on the impact of high-fidelity simulation in an undergraduate setting