Dynamical weather and climate prediction models underpin many studies of the Earth system and hold the promise of being able to make robust projections of future climate change based on physical laws. However, simulations from these models still show many differences compared with observations. Machine learning has been applied to solve certain prediction problems with great success, and recently it's been proposed that this could replace the role of physically-derived dynamical weather and climate models to give better quality simulations. Here, instead, a framework using machine learning together with physically-derived models is tested, in which it is learnt how to correct the errors of the latter from timestep to timestep. This maintains the physical understanding built into the models, whilst allowing performance improvements, and also requires much simpler algorithms and less training data. This is tested in the context of simulating the chaotic Lorenz '96 system, and it is shown that the approach yields models that are stable and that give both improved skill in initialised predictions and better long-term climate statistics. Improvements in long-term statistics are smaller than for single time-step tendencies, however, indicating that it would be valuable to develop methods that target improvements on longer time scales. Future strategies for the development of this approach and possible applications to making progress on important scientific problems are discussed.

There are three quite distinct ways to train a machine learning model on recommender system logs. The first method is to model the reward prediction for each possible recommendation to the user, at the scoring time the best recommendation is found by computing an argmax over the personalized recommendations. This method obeys principles such as the conditionality principle and the likelihood principle. A second method is useful when the model does not fit reality and underfits. In this case, we can use the fact that we know the distribution of historical recommendations (concentrated on previously identified good actions with some exploration) to adjust the errors in the fit to be evenly distributed over all actions. Finally, the inverse propensity score can be used to produce an estimate of the decision rules expected performance. The latter two methods violate the conditionality and likelihood principle but are shown to have good performance in certain settings. In this paper we review the literature around this fundamental, yet often overlooked choice and do some experiments using the RecoGym simulation environment.

Recursive stochastic algorithms have gained significant attention in the recent past due to data driven applications. Examples include stochastic gradient descent for solving large-scale optimization problems and empirical dynamic programming algorithms for solving Markov decision problems. These recursive stochastic algorithms approximates certain contraction operators and can be viewed within the framework of iterated random maps. Accordingly, we consider iterated random maps over a Polish space that simulates a contraction operator over that Polish space. Assume that the iterated maps are indexed by $n$ such that as $n\rightarrow\infty$, each realization of the random map converges (in some sense) to the contraction map it is simulating. We show that starting from the same initial condition, the distribution of the random sequence generated by the iterated random maps converge weakly to the trajectory generated by the contraction operator. We further show that under certain conditions, the time average of the random sequence converge to the spatial mean of the invariant distribution. We then apply these results to logistic regression, empirical value iteration, empirical Q value iteration, and empirical relative value iteration for finite state finite action MDPs.

This paper focuses on a traditional relation extraction task in the context of limited annotated data and a narrow knowledge domain. We explore this task with a clinical corpus consisting of 200 breast cancer follow-up treatment letters in which 16 distinct types of relations are annotated. We experiment with an approach to extracting typed relations called window-bounded co-occurrence (WBC), which uses an adjustable context window around entity mentions of a relevant type, and compare its performance with a more typical intra-sentential co-occurrence baseline. We further introduce a new bag-of-concepts (BoC) approach to feature engineering based on the state-of-the-art word embeddings and word synonyms. We demonstrate the competitiveness of BoC by comparing with methods of higher complexity, and explore its effectiveness on this small dataset.

Model inference, such as model comparison, model checking, and model selection, is an important part of model development. Leave-one-out cross-validation (LOO) is a general approach for assessing the generalizability of a model, but unfortunately, LOO does not scale well to large datasets. We propose a combination of using approximate inference techniques and probability-proportional-to-size-sampling (PPS) for fast LOO model evaluation for large datasets. We provide both theoretical and empirical results showing good properties for large data.

We study online active learning for classifying streaming instances within the framework of statistical learning theory.. At each time, the decision maker decides whether to query for the label of the current instance and, in the event of no query, self labels the instance. The objective is to minimize the number of queries while constraining the number of classification errors over a horizon of length $T$. We consider a general concept space with a finite VC dimension $d$ and adopt the agnostic setting. We propose a disagreement-based online learning algorithm and establish its $O(d\log^2 T)$ label complexity and $\Theta(1)$ (i.e., bounded) classification errors in excess to the best classifier in the concept space under the Massart bounded noise condition.

Continual learning aims to enable machine learning models to learn a general solution space for past and future tasks in a sequential manner. Conventional models tend to forget the knowledge of previous tasks while learning a new task, a phenomenon known as catastrophic forgetting. When using Bayesian models in continual learning, knowledge from previous tasks can be retained in two ways: (i) posterior distributions over the parameters, containing the knowledge gained from inference in previous tasks, which then serve as the priors for the following task; (ii) coresets, containing knowledge of data distributions of previous tasks. Here, we show that Bayesian continual learning can be facilitated in terms of these two means through the use of natural gradients and Stein gradients respectively.

A reliable and accurate forecasting method for crop yields is very important for the farmer, the economy of a country, and the agricultural stakeholders. However, due to weather extremes and uncertainties as a result of increasing climate change, most crop yield forecasting models are not reliable and accurate. In this paper, a hybrid crop yield probability density forecasting method via quantile regression forest and Epanechnikov kernel function (QRF-SJ) is proposed to capture the uncertainties and extremes of weather in crop yield forecasting. By assigning probability to possible crop yield values, probability density forecast gives a complete description of the yield of crops. A case study using the annual crop yield of groundnut and millet in Ghana is presented to illustrate the efficiency and robustness of the proposed technique. The proposed model is able to capture the nonlinearity between crop yield and the weather variables via random forest. The values of prediction interval coverage probability and prediction interval normalized average width for the two crops show that the constructed prediction intervals cover the target values with perfect probability. The probability density curves show that QRF-SJ method has a very high ability to forecast quality prediction intervals with a higher coverage probability. The feature importance gave a score of the importance of each weather variable in building the quantile regression forest model. The farmer and other stakeholders are able to realize the specific weather variable that affect the yield of a selected crop through feature importance. The proposed method and its application on crop yield dataset is the first of its kind in literature.

Sparse PCA has shown its effectiveness in high dimensional data analysis, while there is still a gap between the computational method and statistical theory. This paper presents algorithms to solve the row-sparsity constrained PCA, named Feature Sparse PCA (FSPCA), which performs feature selection and PCA simultaneously. Existing techniques to solve the FSPCA problem suffer two main drawbacks: (1) most approaches only solve the leading eigenvector and rely on the deflation technique to estimate the leading m eigenspace, which has feature sparsity inconsistence, identifiability, and orthogonality issues; (2) some approaches are heuristics without convergence guarantee. In this paper, we present convergence guaranteed algorithms to directly estimate the leading m eigenspace. In detail, we show for a low rank covariance matrix, the FSPCA problem can be solved globally (Algorithm 1). Then, we propose an algorithm (Algorithm 2) to solve the FSPCA for general covariance by iteratively building a carefully designed low rank proxy covariance. Theoretical analysis gives the convergence guarantee. Experimental results show the promising performance of the new algorithms compared with the state-of-the-art method on both synthetic and real-world datasets.

Multimodal learning has been lacking principled ways of combining information from different modalities and learning a low-dimensional manifold of meaningful representations. We study multimodal learning and sensor fusion from a latent variable perspective. We first present a regularized recurrent attention filter for sensor fusion. This algorithm can dynamically combine information from different types of sensors in a sequential decision making task. Each sensor is bonded with a modular neural network to maximize utility of its own information. A gating modular neural network dynamically generates a set of mixing weights for outputs from sensor networks by balancing utility of all sensors' information. We design a co-learning mechanism to encourage co-adaption and independent learning of each sensor at the same time, and propose a regularization based co-learning method. In the second part, we focus on recovering the manifold of latent representation. We propose a co-learning approach using probabilistic graphical model which imposes a structural prior on the generative model: multimodal variational RNN (MVRNN) model, and derive a variational lower bound for its objective functions. In the third part, we extend the siamese structure to sensor fusion for robust acoustic event detection. We perform experiments to investigate the latent representations that are extracted; works will be done in the following months. Our experiments show that the recurrent attention filter can dynamically combine different sensor inputs according to the information carried in the inputs. We consider MVRNN can identify latent representations that are useful for many downstream tasks such as speech synthesis, activity recognition, and control and planning. Both algorithms are general frameworks which can be applied to other tasks where different types of sensors are jointly used for decision making.