Ensembles of climate models are commonly used to improve climate predictions and assess the uncertainties associated with them. Weighting the models according to their performances holds the promise of further improving their predictions. Here, we use an ensemble of decadal climate predictions to demonstrate the ability of sequential learning algorithms (SLAs) to reduce the forecast errors and reduce the uncertainties. Three different SLAs are considered, and their performances are compared with those of an equally weighted ensemble, a linear regression and the climatology. Predictions of four different variables--the surface temperature, the zonal and meridional wind, and pressure--are considered. The spatial distributions of the performances are presented, and the statistical significance of the improvements achieved by the SLAs is tested. Based on the performances of the SLAs, we propose one to be highly suitable for the improvement of decadal climate predictions.

We propose a globally convergent alternating minimization (AM) algorithm for image reconstruction in transmission tomography, which extends automatic relevance determination (ARD) to Poisson noise models with Beer's law. The algorithm promotes solutions that are sparse in the pixel/voxel-differences domain by introducing additional latent variables, one for each pixel/voxel, and then learning these variables from the data using a hierarchical Bayesian model. Importantly, the proposed AM algorithm is free of any tuning parameters with image quality comparable to standard penalized likelihood methods. Our algorithm exploits optimization transfer principles which reduce the problem into parallel 1D optimization tasks (one for each pixel/voxel), making the algorithm feasible for large-scale problems. This approach considerably reduces the computational bottleneck of ARD associated with the posterior variances. Positivity constraints inherent in transmission tomography problems are also enforced. We demonstrate the performance of the proposed algorithm for x-ray computed tomography using synthetic and real-world datasets. The algorithm is shown to have much better performance than prior ARD algorithms based on approximate Gaussian noise models, even for high photon flux.

There has been a recent interest in understanding the power of local algorithms for optimization and inference problems on sparse graphs. Gamarnik and Sudan (2014) showed that local algorithms are weaker than global algorithms for finding large independent sets in sparse random regular graphs. Montanari (2015) showed that local algorithms are suboptimal for finding a community with high connectivity in the sparse Erd\H{o}s-R\'enyi random graphs. For the symmetric planted partition problem (also named community detection for the block models) on sparse graphs, a simple observation is that local algorithms cannot have non-trivial performance. In this work we consider the effect of side information on local algorithms for community detection under the binary symmetric stochastic block model. In the block model with side information each of the $n$ vertices is labeled $+$ or $-$ independently and uniformly at random; each pair of vertices is connected independently with probability $a/n$ if both of them have the same label or $b/n$ otherwise. The goal is to estimate the underlying vertex labeling given 1) the graph structure and 2) side information in the form of a vertex labeling positively correlated with the true one. Assuming that the ratio between in and out degree $a/b$ is $\Theta(1)$ and the average degree $ (a+b) / 2 = n^{o(1)}$, we characterize three different regimes under which a local algorithm, namely, belief propagation run on the local neighborhoods, maximizes the expected fraction of vertices labeled correctly. Thus, in contrast to the case of symmetric block models without side information, we show that local algorithms can achieve optimal performance for the block model with side information.

This paper is concerned with a lesser-studied problem in the context of model-based, uncertainty quantification (UQ), that of optimization/design/control under uncertainty. The solution of such problems is hindered not only by the usual difficulties encountered in UQ tasks (e.g. the high computational cost of each forward simulation, the large number of random variables) but also by the need to solve a nonlinear optimization problem involving large numbers of design variables and potentially constraints. We propose a framework that is suitable for a large class of such problems and is based on the idea of recasting them as probabilistic inference tasks. To that end, we propose a Variational Bayesian (VB) formulation and an iterative VB-Expectation-Maximization scheme that is also capable of identifying a low-dimensional set of directions in the design space, along which, the objective exhibits the largest sensitivity. We demonstrate the validity of the proposed approach in the context of two numerical examples involving $\mathcal{O}(10^3)$ random and design variables. In all cases considered the cost of the computations in terms of calls to the forward model was of the order $\mathcal{O}(10^2)$. The accuracy of the approximations provided is assessed by appropriate information-theoretic metrics.

This report is concerned with the Mondrian process and its applications in machine learning. The Mondrian process is a guillotine-partition-valued stochastic process that possesses an elegant self-consistency property. The first part of the report uses simple concepts from applied probability to define the Mondrian process and explore its properties. The Mondrian process has been used as the main building block of a clever online random forest classification algorithm that turns out to be equivalent to its batch counterpart. We outline a slight adaptation of this algorithm to regression, as the remainder of the report uses regression as a case study of how Mondrian processes can be utilized in machine learning. In particular, the Mondrian process will be used to construct a fast approximation to the computationally expensive kernel ridge regression problem with a Laplace kernel. The complexity of random guillotine partitions generated by a Mondrian process and hence the complexity of the resulting regression models is controlled by a lifetime hyperparameter. It turns out that these models can be efficiently trained and evaluated for all lifetimes in a given range at once, without needing to retrain them from scratch for each lifetime value. This leads to an efficient procedure for determining the right model complexity for a dataset at hand. The limitation of having a single lifetime hyperparameter will motivate the final Mondrian grid model, in which each input dimension is endowed with its own lifetime parameter. In this model we preserve the property that its hyperparameters can be tweaked without needing to retrain the modified model from scratch.

Conflict-Based Search (CBS) and its enhancements, Meta-Agent CBS and bypassing conflicts are amongst the strongest newly introduced algorithms for Multi-Agent Path Finding. This paper introduces two new improvements to CBS and incorporates them into a coherent, improved version of CBS, namely ICBS. Experimental results show that each of these improvements further reduces the runtime over the existing CBS-based approaches. When all improvements are combined, an even larger improvement is achieved, producing state-of-the art results for a number of domains.

The investigation and development of new methods from diverse perspectives to shed light on portfolio choice problems has never stagnated in financial research. Recently, multi-armed bandits have drawn intensive attention in various machine learning applications in online settings. The tradeoff between exploration and exploitation to maximize rewards in bandit algorithms naturally establishes a connection to portfolio choice problems. In this paper, we present a bandit algorithm for conducting online portfolio choices by effectually exploiting correlations among multiple arms. Through constructing orthogonal portfolios from multiple assets and integrating with the upper confidence bound bandit framework, we derive the optimal portfolio strategy that represents the combination of passive and active investments according to a risk-adjusted reward function. Compared with oft-quoted trading strategies in finance and machine learning fields across representative real-world market datasets, the proposed algorithm demonstrates superiority in both risk-adjusted return and cumulative wealth.

Expectation maximization (EM) has recently been shown to be an efficient algorithm for learning finite-state controllers (FSCs) in large decentralized POMDPs (Dec-POMDPs). However, current methods use fixed-size FSCs and often converge to maxima that are far from the optimal value. This paper considers a variable-size FSC to represent the local policy of each agent. These variable-size FSCs are constructed using a stick-breaking prior, leading to a new framework called decentralized stick-breaking policy representation (Dec-SBPR). This approach learns the controller parameters with a variational Bayesian algorithm without having to assume that the Dec-POMDP model is available. The performance of Dec-SBPR is demonstrated on several benchmark problems, showing that the algorithm scales to large problems while outperforming other state-of-the-art methods.

The task of machine condition monitoring is to detect machine failures at an early stage such that maintenance can be carried out in a timely manner. Most existing techniques are supervised approaches: they require user annotated training data to learn normal and faulty behaviors of a machine. However, such supervision can be difficult to acquire. In contrast, unsupervised methods don't need much human involvement, however, they face another challenge: how to model the generative (observation) process of sensor signals. We propose an unsupervised approach based on segmental hidden Markov models. Our method has a unifying observation model integrating three pieces of information that are complementary to each other. First, we model the signal as an explicit function over time, which describes its possible non-stationary trending patterns. Second, the stationary part of the signal is fit by an autoregressive model. Third, we introduce contextual information to break down the signal complexity such that the signal is modeled separately under different conditions. The advantages of the proposed model are demonstrated by tests on gas turbine, truck and honeybee datasets.

Exploration strategy is an essential part of learning agents in model-based Reinforcement Learning. R-MAX and V-MAX are PAC-MDP strategies proved to have polynomial sample complexity; yet, their exploration behavior tend to be overly cautious in practice. We propose the principle of Increasingly Cautious Optimism (ICO) to automatically cut off unnecessarily cautious exploration, and apply ICO to R-MAX and V-MAX, yielding two new strategies, namely Increasingly Cautious R-MAX (ICR) and Increasingly Cautious V-MAX (ICV). We prove that both ICR and ICV are PACMDP, and show that their improvement is guaranteed by a tighter sample complexity upper bound. Then, we demonstrate their significantly improved performance through empirical results.