Estimation of Markov Chain via Rank-Constrained Likelihood

This paper studies the estimation of low-rank Markov chains from empirical trajectories. We propose a non-convex estimator based on rank-constrained likelihood maximization. Statistical upper bounds are provided for the Kullback-Leiber divergence and the $\ell_2$ risk between the estimator and the true transition matrix. The estimator reveals a compressed state space of the Markov chain. We also develop a novel DC (difference of convex function) programming algorithm to tackle the rank-constrained non-smooth optimization problem. Convergence results are established. Experiments show that the proposed estimator achieves better empirical performance than other popular approaches.Comment: Accepted at ICML 201

Diffusion Approximations for Online Principal Component Estimation and Global Convergence

In this paper, we propose to adopt the diffusion approximation tools to study the dynamics of Oja's iteration which is an online stochastic gradient descent method for the principal component analysis. Oja's iteration maintains a running estimate of the true principal component from streaming data and enjoys less temporal and spatial complexities. We show that the Oja's iteration for the top eigenvector generates a continuous-state discrete-time Markov chain over the unit sphere. We characterize the Oja's iteration in three phases using diffusion approximation and weak convergence tools. Our three-phase analysis further provides a finite-sample error bound for the running estimate, which matches the minimax information lower bound for principal component analysis under the additional assumption of bounded samples.Comment: Appeared in NIPS 201

A sensitive and rapid HPLC-DAD method for the determination of 3-hydroxy-1,2-dimethyl-4-pyridone and its distribution in rats

Purpose: To establish a sensitive and rapid method for the determination of the tissue distribution of 3-hydroxy-1,2-dimethyl-4-pyridone (L1) in vivo, and its plasma protein binding capacity.Methods: This study optimized a reverse-phase HPLC method for specific and sensitive determination of L1 as well as its plasma and tissue  distributions. The optimized method was used to determine the plasma protein-binding capacity of L1 in Wistar rats.Results: A rapid, sensitive and simple HPLC-DAD method was established for studying the plasma and tissue distribution of L1. Following TI  administration, its liver concentrations peaked at 60 min and 360min, followed 360 min later with peak level in the kidney (second highest). The L1 concentration was significantly lower after 360 min than after 60 min, and values of its mean binding to plasma proteins was 5.2 % at different L1 concentrations.Conclusion: These results indicate that L1 is a drug with rapid-absorption and rapid-elimination thath is distributed widely in vivo in rats. Moreover, the drug has a weak plasma protein-binding capacity. Keywords: 3-Hydroxy-1,2-dimethyl-4-pyridone, Distribution, Alzheimer’s disease, Therap

Stochastic modelling and optimization with applications to actuarial models

This thesis is devoted to Ruin Theory which sometimes referred to the collective ruin theory. In Actuarial Science, one of the most important problems is to determine the finite time or infinite time ruin probability of the risk process in an insurance company. To treat a realistic economic situation, the random interest factor should be taken into account. We first define the model with the interest rate and approximate the ruin probability for the model by the Brownian motion and develop several numerical methods to evaluate the ruin probability. Then we construct several models which incorporate possible investment strategies. We estimate the parameters from the simulated data. Then we find the optimal investment strategy with a given upper bound on the ruin probability. Finally we study the ruin probability for our class of models with the Heavy- Tailed claim size distribution

Twitter sentiment analysis in the era of emojis

Twitter has become an important site for national discussions where we can get a new and timely update of the public opinion towards any event. Twitter Sentiment Analysis (TSA) can be an effective method for unpacking the deep insights embodied within the opinions of the public. Recently, various TSA techniques have been developed, but little consideration has gone into emojis, which is a new invention and has been popularly shared by Twitter users from different countries, with various demographic characteristics, and diverse cultural backgrounds. The ubiquitous adoption of emojis on Twitter provides new opportunities to analyse sentiment expressions in a textual context. Emojis should be included when conducting TSA as the meaning of a Twitter post and its sentiment can be identified with greater clarity and accuracy with emojis. This research aims to develop novel approaches that handle emojis properly and tackle current open issues in TSA. Consisting of four phases, this thesis presents a comprehensive and in-depth research work in the field of Emoji Analytics and TSA. Several studies have been conducted to investigate emoji usage on Twitter and evaluate their effects on TSA. The experimental results demonstrate that emojis has become an essential component of Twitter communication and it is an important area of study complementary to TSA, implying promising future research opportunities for TSA. A novel TSA methodological framework that collects, pre-processes, analyses and maps citizen sentiments from Twitter in helping learn citizens’ moods has been implemented and proved to be effective. The novel framework identifies the best setting for TSA when involving emojis, and proposes an effective emoji training heuristic, which is feasible for both ternary and multi-class classification of tweets. Besides, it innovatively includes the visualisation of user-generated contents in a location-based manner on geographical maps, which provides a much easier-to-understand visual representation of the sentiment. The methodological framework has been proved applicable in real-world scenarios and can be used to support research in other fields. Being the first to consider popularity of emojis on Twitter and include them in performing TSA, this research is considered to be a pioneering work in the field, suggesting a new direction for TSA in the era of emojis

Determinants of Capital Structure of Chinese Listed Firms

This paper aims to study and identify the determinants of the company's capital structure and analyze which capital structure theory is more relevant and applicable to Chinese listed companies. The sample for this study involves 56 Chinese listed companies from 2009 to 2016 in five industries in the Shenzhen stock exchange (SZSE) from the database CSMAR (China Securities Market and Accounting Research). The panel data regression has been used to analyze the impact of capital structure on the companies. The profitability, size, growth opportunities, tangibility, non-debt tax shields and inflation could be as the independent variables. The research is to test the relationship between six variables and two leverages. According to our research, most of the determinants follow the prediction of theories, such as size, growth opportunities, profitability and non-debt tax shields, but the tangibility has the different prediction. On the contrary, the inflation is proved to not have a significant sign with the long-term and short-term leverage, which means the inflation does not have any right to interpret Chinese companies financing option