I do really appreciate these helpful on-hand labs and lectures. Passed the DP-100 in Dec 2020.

The titanic is one of the most iconic and at the same time saddest stories in the history of human beings. There are barely any individuals who are not familiar with its story and how lucky some people were on that liner, because of certain characteristics that they took with them. Whether they were kids or had a higher purchasing power, there was a pattern to follow when predicting the probability of getting a safe boat, leaving unharmed the ship. The cleaning of the data is by far the most challenging part in most of the machine learning projects since you can extremely improve (or harm) your model according to the individual features and the types of features you train your model with. For feature selection, we will go through three main aspects.

Recent advance in machine learning has made face recognition not a difficult problem. But in the previous, researchers have made various attempts and developed various skills to make computer capable of identifying people. One of the early attempt with moderate success is eigenface, which is based on linear algebra techniques. In this tutorial, we will see how we can build a primitive face recognition system with some simple linear algebra technique such as principal component analysis. Face Recognition using Principal Component Analysis Photo by Rach Teo, some rights reserved.

Each of the four weeks in the course will consist of two required components. First, an interactive textbook provides Python programming challenges that arise from real biological problems. If you haven't programmed in Python before, not to worry! We provide "Just-in-Time" exercises from the Codecademy Python track (https://www.codecademy.com/learn/python). And each page in our interactive textbook has its own discussion forum, where you can interact with other learners.

Precision medicine is a clinical approach for disease prevention, detection and treatment, which considers each individual's genetic background, environment and lifestyle. The development of this tailored avenue has been driven by the increased availability of omics methods, large cohorts of temporal samples, and their integration with clinical data. Despite the immense progression, existing computational methods for data analysis fail to provide appropriate solutions for this complex, high-dimensional and longitudinal data. In this work we have developed a new method termed TCAM, a dimensionality reduction technique for multi-way data, that overcomes major limitations when doing trajectory analysis of longitudinal omics data. Using real-world data, we show that TCAM outperforms traditional methods, as well as state-of-the-art tensor-based approaches for longitudinal microbiome data analysis. Moreover, we demonstrate the versatility of TCAM by applying it to several different omics datasets, and the applicability of it as a drop-in replacement within straightforward ML tasks.

In recent years, large-scale Bayesian learning draws a great deal of attention. However, in big-data era, the amount of data we face is growing much faster than our ability to deal with it. Fortunately, it is observed that large-scale datasets usually own rich internal structure and is somewhat redundant. In this paper, we attempt to simplify the Bayesian posterior via exploiting this structure. Specifically, we restrict our interest to the so-called well-clustered datasets and construct an \emph{approximate posterior} according to the clustering information. Fortunately, the clustering structure can be efficiently obtained via a particular clustering algorithm. When constructing the approximate posterior, the data points in the same cluster are all replaced by the centroid of the cluster. As a result, the posterior can be significantly simplified. Theoretically, we show that under certain conditions the approximate posterior we construct is close (measured by KL divergence) to the exact posterior. Furthermore, thorough experiments are conducted to validate the fact that the constructed posterior is a good approximation to the true posterior and much easier to sample from.

Mixture model is a probabilistic model that is able to infer subpopulations from total population without additional information (within the paradigm of unsupervised learning). Mixture models closely correspond to the mixture distributions of the probabilistic distributions of observations. In general, in the structure of mixture model, we make assumptions over latent variables that evaluate membership of each observation. Given the dataset, we can assume that it is a sample and then mixture model can estimate the parameters of the probability distributions that created points of this dataset, as well as assign each observation vector of probabilities indicating the original distribution. Comparing different mixture models can be considered a generalization of the problem of comparing different distributions. From the viewpoint of optimal transport theory, the Wasserstein distance is an important method for measuring similarities and the maintenance of the explainable nature of mixture models.

Escaping saddle points is a central research topic in nonconvex optimization. In this paper, we propose a simple gradient-based algorithm such that for a smooth function $f\colon\mathbb{R}^n\to\mathbb{R}$, it outputs an $\epsilon$-approximate second-order stationary point in $\tilde{O}(\log n/\epsilon^{1.75})$ iterations. Compared to the previous state-of-the-art algorithms by Jin et al. with $\tilde{O}((\log n)^{4}/\epsilon^{2})$ or $\tilde{O}((\log n)^{6}/\epsilon^{1.75})$ iterations, our algorithm is polynomially better in terms of $\log n$ and matches their complexities in terms of $1/\epsilon$. For the stochastic setting, our algorithm outputs an $\epsilon$-approximate second-order stationary point in $\tilde{O}((\log n)^{2}/\epsilon^{4})$ iterations. Technically, our main contribution is an idea of implementing a robust Hessian power method using only gradients, which can find negative curvature near saddle points and achieve the polynomial speedup in $\log n$ compared to the perturbed gradient descent methods. Finally, we also perform numerical experiments that support our results.

Hierarchical models with gamma hyperpriors provide a flexible, sparse-promoting framework to bridge $L^1$ and $L^2$ regularizations in Bayesian formulations to inverse problems. Despite the Bayesian motivation for these models, existing methodologies are limited to \textit{maximum a posteriori} estimation. The potential to perform uncertainty quantification has not yet been realized. This paper introduces a variational iterative alternating scheme for hierarchical inverse problems with gamma hyperpriors. The proposed variational inference approach yields accurate reconstruction, provides meaningful uncertainty quantification, and is easy to implement. In addition, it lends itself naturally to conduct model selection for the choice of hyperparameters. We illustrate the performance of our methodology in several computed examples, including a deconvolution problem and sparse identification of dynamical systems from time series data.

Maximum Entropy Reinforcement Learning (MaxEnt RL) algorithms such as Soft Q-Learning (SQL) and Soft Actor-Critic trade off reward and policy entropy, which has the potential to improve training stability and robustness. Most MaxEnt RL methods, however, use a constant tradeoff coefficient (temperature), contrary to the intuition that the temperature should be high early in training to avoid overfitting to noisy value estimates and decrease later in training as we increasingly trust high value estimates to truly lead to good rewards. Moreover, our confidence in value estimates is state-dependent, increasing every time we use more evidence to update an estimate. In this paper, we present a simple state-based temperature scheduling approach, and instantiate it for SQL as Count-Based Soft Q-Learning (CBSQL). We evaluate our approach on a toy domain as well as in several Atari 2600 domains and show promising results.