In this paper, we analyze maximum Sharpe ratio when the number of assets in a portfolio is larger than its time span. One obstacle in this large dimensional setup is the singularity of the sample covariance matrix of the excess asset returns. To solve this issue, we benefit from a technique called nodewise regression, which was developed by Meinshausen and Buhlmann (2006). It provides a sparse/weakly sparse and consistent estimate of the precision matrix, using the Lasso method. We analyze three issues. One of the key results in our paper is that mean-variance efficiency for the portfolios in large dimensions is established. Then tied to that result, we also show that the maximum out-of-sample Sharpe ratio can be consistently estimated in this large portfolio of assets. Furthermore, we provide convergence rates and see that the number of assets slow down the convergence up to a logarithmic factor. Then, we provide consistency of maximum Sharpe Ratio when the portfolio weights add up to one, and also provide a new formula and an estimate for constrained maximum Sharpe ratio. Finally, we provide consistent estimates of the Sharpe ratios of global minimum variance portfolio and Markowitz's (1952) mean variance portfolio. In terms of assumptions, we allow for time series data. Simulation and out-of-sample forecasting exercise shows that our new method performs well compared to factor and shrinkage based techniques.

We introduce a binary embedding framework, called Proximity Preserving Code (PPC), which learns similarity and dissimilarity between data points to create a compact and affinity-preserving binary code. This code can be used to apply fast and memory-efficient approximation to nearest-neighbor searches. Our framework is flexible, enabling different proximity definitions between data points. In contrast to previous methods that extract binary codes based on unsigned graph partitioning, our system models the attractive and repulsive forces in the data by incorporating positive and negative graph weights. The proposed framework is shown to boil down to finding the minimal cut of a signed graph, a problem known to be NP-hard. We offer an efficient approximation and achieve superior results by constructing the code bit after bit. We show that the proposed approximation is superior to the commonly used spectral methods with respect to both accuracy and complexity. Thus, it is useful for many other problems that can be translated into signed graph cut.

We provide a new online learning algorithm which utilizes online passive-aggressive learning (PA) and total-error-rate minimization (TER) for binary classification. The PA learning establishes not only large margin training but also the capacity to handle non-separable data. The TER learning on the other hand minimizes an approximated classification error based objective function. We propose an online PATER algorithm which combines those useful properties. In addition, we also present a weighted PATER algorithm to improve the ability to cope with data imbalance problems. Experimental results demonstrate that the proposed PATER algorithms achieves better performances in terms of efficiency and effectiveness than the existing state-of-the-art online learning algorithms in real-world data sets.

The Markov assumption (MA) is fundamental to the empirical validity of reinforcement learning. In this paper, we propose a novel Forward-Backward Learning procedure to test MA in sequential decision making. The proposed test does not assume any parametric form on the joint distribution of the observed data and plays an important role for identifying the optimal policy in high-order Markov decision processes and partially observable MDPs. We apply our test to both synthetic datasets and a real data example from mobile health studies to illustrate its usefulness.

Self-exciting Hawkes processes are used to model events which cluster in time and space, and have been widely studied in seismology under the name of the Epidemic Type Aftershock Sequence (ETAS) model. In the ETAS framework, the occurrence of the mainshock earthquakes in a geographical region is assumed to follow an inhomogeneous spatial point process, and aftershock events are then modelled via a separate triggering kernel. Most previous studies of the ETAS model have relied on point estimates of the model parameters due to the complexity of the likelihood function, and the difficulty in estimating an appropriate mainshock distribution. In order to take estimation uncertainty into account, we instead propose a fully Bayesian formulation of the ETAS model which uses a nonparametric Dirichlet process mixture prior to capture the spatial mainshock process. Direct inference for the resulting model is problematic due to the strong correlation of the parameters for the mainshock and triggering processes, so we instead use an auxiliary latent variable routine to perform efficient inference.

Entropy minimization has been widely used in unsupervised domain adaptation (UDA). However, existing works reveal that entropy minimization only may result into collapsed trivial solutions. In this paper, we propose to avoid trivial solutions by further introducing diversity maximization. In order to achieve the possible minimum target risk for UDA, we show that diversity maximization should be elaborately balanced with entropy minimization, the degree of which can be finely controlled with the use of deep embedded validation in an unsupervised manner. The proposed minimal-entropy diversity maximization (MEDM) can be directly implemented by stochastic gradient descent without use of adversarial learning. Empirical evidence demonstrates that MEDM outperforms the state-of-the-art methods on four popular domain adaptation datasets.

Graph matching consists of aligning the vertices of two unlabeled graphs in order to maximize the shared structure across networks; when the graphs are unipartite, this is commonly formulated as minimizing their edge disagreements. In this paper, we address the common setting in which one of the graphs to match is a bipartite network and one is unipartite. Commonly, the bipartite networks are collapsed or projected into a unipartite graph, and graph matching proceeds as in the classical setting. This potentially leads to noisy edge estimates and loss of information. We formulate the graph matching problem between a bipartite and a unipartite graph using an undirected graphical model, and introduce methods to find the alignment with this model without collapsing. In simulations and real data examples, we show how our methods can result in a more accurate matching than the naive approach of transforming the bipartite networks into unipartite, and we demonstrate the performance gains achieved by our method in simulated and real data networks, including a co-authorship-citation network pair and brain structural and functional data.

Automatic music generation is an interdisciplinary research topic that combines computational creativity and semantic analysis of music to create automatic machine improvisations. An important property of such a system is allowing the user to specify conditions and desired properties of the generated music. In this paper we designed a model for composing melodies given a user specified symbolic scenario combined with a previous music context. We add manual labeled vectors denoting external music quality in terms of chord function that provides a low dimensional representation of the harmonic tension and resolution. Our model is capable of generating long melodies by regarding 8-beat note sequences as basic units, and shares consistent rhythm pattern structure with another specific song. The model contains two stages and requires separate training where the first stage adopts a Conditional Variational Autoencoder (C-VAE) to build a bijection between note sequences and their latent representations, and the second stage adopts long short-term memory networks (LSTM) with structural conditions to continue writing future melodies. We further exploit the disentanglement technique via C-VAE to allow melody generation based on pitch contour information separately from conditioning on rhythm patterns. Finally, we evaluate the proposed model using quantitative analysis of rhythm and the subjective listening study. Results show that the music generated by our model tends to have salient repetition structures, rich motives, and stable rhythm patterns. The ability to generate longer and more structural phrases from disentangled representations combined with semantic scenario specification conditions shows a broad application of our model.

Causal inference is a critical research topic across many domains, such as statistics, computer science, education, public policy and economics, for decades. Nowadays, estimating causal effect from observational data has become an appealing research direction owing to the large amount of available data and low budget requirement, compared with randomized controlled trials. Embraced with the rapidly developed machine learning area, various causal effect estimation methods for observational data have sprung up. In this survey, we provide a comprehensive review of causal inference methods under the potential outcome framework, one of the well known causal inference framework. The methods are divided into two categories depending on whether they require all three assumptions of the potential outcome framework or not. For each category, both the traditional statistical methods and the recent machine learning enhanced methods are discussed and compared. The plausible applications of these methods are also presented, including the applications in advertising, recommendation, medicine and so on. Moreover, the commonly used benchmark datasets as well as the open-source codes are also summarized, which facilitate researchers and practitioners to explore, evaluate and apply the causal inference methods.

Hierarchical reinforcement learning (HRL) helps address large-scale and sparse reward issues in reinforcement learning. In HRL, the policy model has an inner representation structured in levels. With this structure, the reinforcement learning task is expected to be decomposed into corresponding levels with sub-tasks, and thus the learning can be more efficient. In HRL, although it is intuitive that a high-level policy only needs to make macro decisions in a low frequency, the exact frequency is hard to be simply determined. Previous HRL approaches often employed a fixed-time skip strategy or learn a terminal condition without taking account of the context, which, however, not only requires manual adjustments but also sacrifices some decision granularity. In this paper, we propose the \emph{temporal-adaptive hierarchical policy learning} (TEMPLE) structure, which uses a temporal gate to adaptively control the high-level policy decision frequency. We train the TEMPLE structure with PPO and test its performance in a range of environments including 2-D rooms, Mujoco tasks, and Atari games. The results show that the TEMPLE structure can lead to improved performance in these environments with a sequential adaptive high-level control.