One of the current challenges in machine learning is how to deal with data coming at increasing rates in data streams. New predictive learning strategies are needed to cope with the high throughput data and concept drift. One of the data stream mining tasks where new learning strategies are needed is multi-target regression, due to its applicability in a high number of real world problems. While reliable and effective learning strategies have been proposed for batch multi-target regression, few have been proposed for multi-target online learning in data streams. Besides, the existing solutions do not consider the occurrence of inter-target correlations when making predictions. In this work, we propose an online learning strategy for multi-target regression in data streams. The proposed strategy extends a single target decision tree online learning algorithm to allow multi-target online regression learning in data streams. For such, the proposed strategy, called Stacked Single-target Hoeffding Tree (SST-HT), uses the inter-target dependencies as an additional information source to enhance predictive accuracy. Throughout an extensive experimental setup, we evaluate our proposal against state-of-the-art decision tree-based algorithms for online multi-target regression. According to the experimental results, SST-HT presents superior predictive accuracy, with a small increase in the processing time and memory requirements.
From @math it is possible to obtain a prediction @math for a instance @math . When constructing @math one expects that the obtained values of @math are as close as possible to the real measured target values @math . Regarding algorithmic solutions, accordingly to @cite_5 MTR problems have been solved using two main strategies for the solutions: global methods and local methods. Global methods correspond to solutions that use a single model to predict all target variables at once. Those methods implicitly model the inter-target dependencies, and also offer more compact and less computationally costly solutions for MTR tasks, being more viable to online scenarios. The local methods, on the other hand, employ traditional STR solutions and often manipulate or modify the input space to insert the inter-target dependency information within the problem modelling. In this sense, local methods use multiple ST regressors to solve a MTR task, frequently more than one regressor for each target variable , which in turn make them more costly solutions than the global ones. The simplest local solution for MTR tasks, as previously mentioned, consists in creating a ST regressor for each target and simply ignoring the underlying inter-target dependencies.
@cite_5
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Many real life prediction problems involve predicting a structured output. Multi-target regression is an instance of structured output prediction whose task is to predict for multiple target variables. Structured output algorithms are usually computationally and memory demanding, hence are not suited for dealing with massive amounts of data. Most of these algorithms can be categorized as local or global methods. Local methods produce individual models for each output component and combine them to produce the structured prediction. Global methods adapt traditional learning algorithms to predict the output structure as a whole. We propose the first rule-based algorithm for solving multi-target regression problems from data streams. The algorithm builds on the adaptive model rules framework. In contrast to the majority of the structured output predictors, this particular algorithm does not fall into the local and global categories. Instead, each rule specializes on related subsets of the output attributes. To evaluate the performance of the proposed algorithm, two other rule-based algorithms were developed, one using the local strategy and the other using the global strategy. These methods were compared considering their prediction error, memory usage, computational time, and model complexity. Experimental results on synthetic and real data show that the local-strategy algorithm usually obtains the lowest error. However, the proposed and the global-strategy algorithms use much less memory and run significantly much faster at the cost of a slightly increase in the error, which make them very attractive when computation resources are an important factor. Also, the models produced by the latter approaches are much easier to understand since considerably less rules are produced. In this paper, we formulate object tracking in a particle filter framework as a structured multi-task sparse learning problem, which we denote as Structured Multi-Task Tracking (S-MTT). Since we model particles as linear combinations of dictionary templates that are updated dynamically, learning the representation of each particle is considered a single task in Multi-Task Tracking (MTT). By employing popular sparsity-inducing @math mixed norms @math and @math we regularize the representation problem to enforce joint sparsity and learn the particle representations together. As compared to previous methods that handle particles independently, our results demonstrate that mining the interdependencies between particles improves tracking performance and overall computational complexity. Interestingly, we show that the popular @math tracker (Mei and Ling, IEEE Trans Pattern Anal Mach Intel 33(11):2259---2272, 2011) is a special case of our MTT formulation (denoted as the @math tracker) when @math Under the MTT framework, some of the tasks (particle representations) are often more closely related and more likely to share common relevant covariates than other tasks. Therefore, we extend the MTT framework to take into account pairwise structural correlations between particles (e.g. spatial smoothness of representation) and denote the novel framework as S-MTT. The problem of learning the regularized sparse representation in MTT and S-MTT can be solved efficiently using an Accelerated Proximal Gradient (APG) method that yields a sequence of closed form updates. As such, S-MTT and MTT are computationally attractive. We test our proposed approach on challenging sequences involving heavy occlusion, drastic illumination changes, and large pose variations. Experimental results show that S-MTT is much better than MTT, and both methods consistently outperform state-of-the-art trackers. When we have several related tasks, solving them simultaneously is shown to be more effective than solving them individually. This approach is called multi-task learning (MTL) and has been studied extensively. Existing approaches to MTL often treat all the tasks as uniformly related to each other and the relatedness of the tasks is controlled globally. For this reason, the existing methods can lead to undesired solutions when some tasks are not highly related to each other, and some pairs of related tasks can have significantly different solutions. In this paper, we propose a novel MTL algorithm that can overcome these problems. Our method makes use of a task network, which describes the relation structure among tasks. This allows us to deal with intricate relation structures in a systematic way. Furthermore, we control the relatedness of the tasks locally, so all pairs of related tasks are guaranteed to have similar solutions. We apply the above idea to support vector machines (SVMs) and show that the optimization problem can be cast as a second order cone program, which is convex and can be solved efficiently. The usefulness of our approach is demonstrated through simulations with protein super-family classification and ordinal regression problems. We consider the problem of learning a one-hidden-layer neural network: we assume the input @math is from Gaussian distribution and the label @math , where @math is a nonnegative vector in @math with @math , @math is a full-rank weight matrix, and @math is a noise vector. We first give an analytic formula for the population risk of the standard squared loss and demonstrate that it implicitly attempts to decompose a sequence of low-rank tensors simultaneously. Inspired by the formula, we design a non-convex objective function @math whose landscape is guaranteed to have the following properties: 1. All local minima of @math are also global minima. 2. All global minima of @math correspond to the ground truth parameters. 3. The value and gradient of @math can be estimated using samples. With these properties, stochastic gradient descent on @math provably converges to the global minimum and learn the ground-truth parameters. We also prove finite sample complexity result and validate the results by simulations.