We tackle the problem of multi-task learning with copula process. Multivariable prediction in spatial and spatial-temporal processes such as natural resource estimation and pollution monitoring have been typically addressed using techniques based on Gaussian processes and co-Kriging. While the Gaussian prior assumption is convenient from analytical and computational perspectives, nature is dominated by non-Gaussian likelihoods. Copula processes are an elegant and flexible solution to handle various non-Gaussian likelihoods by capturing the dependence structure of random variables with cumulative distribution functions rather than their marginals. We show how multi-task learning for copula processes can be used to improve multivariable prediction for problems where the simple Gaussianity prior assumption does not hold. Then, we present a transductive approximation for multi-task learning and derive analytical expressions for the copula process model. The approach is evaluated and compared to other techniques in one artificial dataset and two publicly available datasets for natural resource estimation and concrete slump prediction.
Learning object detectors requires massive amounts of labeled training samples from the specific data source of interest. This is impractical when dealing with many different sources (e.g., in camera networks), or constantly changing ones such as mobile cameras (e.g., in robotics or driving assistant systems). In this paper, we address the problem of self-learning detectors in an autonomous manner, i.e. (i) detectors continuously updating themselves to efficiently adapt to streaming data sources (contrary to transductive algorithms), (ii) without any labeled data strongly related to the target data stream (contrary to self-paced learning), and (iii) without manual intervention to set and update hyper-parameters. To that end, we propose an unsupervised, on-line, and self-tuning learning algorithm to optimize a multi-task learning convex objective. Our method uses confident but laconic oracles (high-precision but low-recall off-the-shelf generic detectors), and exploits the structure of the problem to jointly learn on-line an ensemble of instance-level trackers, from which we derive an adapted category-level object detector. Our approach is validated on real-world publicly available video object datasets.
We propose an heterogeneous multi-task learning framework for human pose estimation from monocular image with deep convolutional neural network. In particular, we simultaneously learn a pose-joint regressor and a sliding-window body-part detector in a deep network architecture. We show that including the body-part detection task helps to regularize the network, directing it to converge to a good solution. We report competitive and state-of-art results on several data sets. We also empirically show that the learned neurons in the middle layer of our network are tuned to localized body parts.
In this paper, we investigate the statistical convergence rate of a Bayesian low-rank tensor estimator. Our problem setting is the regression problem where a tensor structure underlying the data is estimated. This problem setting occurs in many practical applications, such as collaborative filtering, multi-task learning, and spatio-temporal data analysis. The convergence rate is analyzed in terms of both in-sample and out-of-sample predictive accuracies. It is shown that a near optimal rate is achieved without any strong convexity of the observation. Moreover, we show that the method has adaptivity to the unknown rank of the true tensor, that is, the near optimal rate depending on the true rank is achieved even if it is not known a priori.
In this paper, we study the generalization performance of regularized multi-task learning (RMTL) in a vector-valued framework, where MTL is considered as a learning process for vector-valued functions. We are mainly concerned with two theoretical questions: 1) under what conditions does RMTL perform better with a smaller task sample size than STL? 2) under what conditions is RMTL generalizable and can guarantee the consistency of each task during simultaneous learning? In particular, we investigate two types of task-group relatedness: the observed discrepancy-dependence measure (ODDM) and the empirical discrepancy-dependence measure (EDDM), both of which detect the dependence between two groups of multiple related tasks (MRTs). We then introduce the Cartesian product-based uniform entropy number (CPUEN) to measure the complexities of vector-valued function classes. By applying the specific deviation and the symmetrization inequalities to the vector-valued framework, we obtain the generalization bound for RMTL, which is the upper bound of the joint probability of the event that there is at least one task with a large empirical discrepancy between the expected and empirical risks. Finally, we present a sufficient condition to guarantee the consistency of each task in the simultaneous learning process, and we discuss how task relatedness affects the generalization performance of RMTL. Our theoretical findings answer the aforementioned two questions.
Traditionally, Multi-task Learning (MTL) models optimize the average of task-related objective functions, which is an intuitive approach and which we will be referring to as Average MTL. However, a more general framework, referred to as Conic MTL, can be formulated by considering conic combinations of the objective functions instead; in this framework, Average MTL arises as a special case, when all combination coefficients equal 1. Although the advantage of Conic MTL over Average MTL has been shown experimentally in previous works, no theoretical justification has been provided to date. In this paper, we derive a generalization bound for the Conic MTL method, and demonstrate that the tightest bound is not necessarily achieved, when all combination coefficients equal 1; hence, Average MTL may not always be the optimal choice, and it is important to consider Conic MTL. As a byproduct of the generalization bound, it also theoretically explains the good experimental results of previous relevant works. Finally, we propose a new Conic MTL model, whose conic combination coefficients minimize the generalization bound, instead of choosing them heuristically as has been done in previous methods. The rationale and advantage of our model is demonstrated and verified via a series of experiments by comparing with several other methods.
Multi-task learning (MTL) aims to improve generalization performance by learning multiple related tasks simultaneously. While sometimes the underlying task relationship structure is known, often the structure needs to be estimated from data at hand. In this paper, we present a novel family of models for MTL, applicable to regression and classification problems, capable of learning the structure of task relationships. In particular, we consider a joint estimation problem of the task relationship structure and the individual task parameters, which is solved using alternating minimization. The task relationship structure learning component builds on recent advances in structure learning of Gaussian graphical models based on sparse estimators of the precision (inverse covariance) matrix. We illustrate the effectiveness of the proposed model on a variety of synthetic and benchmark datasets for regression and classification. We also consider the problem of combining climate model outputs for better projections of future climate, with focus on temperature in South America, and show that the proposed model outperforms several existing methods for the problem.
Multi-task learning (MTL) improves prediction performance in different contexts by learning models jointly on multiple different, but related tasks. Network data, which are a priori data with a rich relational structure, provide an important context for applying MTL. In particular, the explicit relational structure implies that network data is not i.i.d. data. Network data also often comes with significant metadata (i.e., attributes) associated with each entity (node). Moreover, due to the diversity and variation in network data (e.g., multi-relational links or multi-category entities), various tasks can be performed and often a rich correlation exists between them. Learning algorithms should exploit all of these additional sources of information for better performance. In this work we take a metric-learning point of view for the MTL problem in the network context. Our approach builds on structure preserving metric learning (SPML). In particular SPML learns a Mahalanobis distance metric for node attributes using network structure as supervision, so that the learned distance function encodes the structure and can be used to predict link patterns from attributes. SPML is described for single-task learning on single network. Herein, we propose a multi-task version of SPML, abbreviated as MT-SPML, which is able to learn across multiple related tasks on multiple networks via shared intermediate parametrization. MT-SPML learns a specific metric for each task and a common metric for all tasks. The task correlation is carried through the common metric and the individual metrics encode task specific information. When combined together, they are structure-preserving with respect to individual tasks. MT-SPML works on general networks, thus is suitable for a wide variety of problems. In experiments, we challenge MT-SPML on two real-word problems, where MT-SPML achieves significant improvement.
We investigate architectures of discriminatively trained deep Convolutional Networks (ConvNets) for action recognition in video. The challenge is to capture the complementary information on appearance from still frames and motion between frames. We also aim to generalise the best performing hand-crafted features within a data-driven learning framework. Our contribution is three-fold. First, we propose a two-stream ConvNet architecture which incorporates spatial and temporal networks. Second, we demonstrate that a ConvNet trained on multi-frame dense optical flow is able to achieve very good performance in spite of limited training data. Finally, we show that multi-task learning, applied to two different action classification datasets, can be used to increase the amount of training data and improve the performance on both. Our architecture is trained and evaluated on the standard video actions benchmarks of UCF-101 and HMDB-51, where it is competitive with the state of the art. It also exceeds by a large margin previous attempts to use deep nets for video classification.
Sharing information between multiple tasks enables algorithms to achieve good generalization performance even from small amounts of training data. However, in a realistic scenario of multi-task learning not all tasks are equally related to each other, hence it could be advantageous to transfer information only between the most related tasks. In this work we propose an approach that processes multiple tasks in a sequence with sharing between subsequent tasks instead of solving all tasks jointly. Subsequently, we address the question of curriculum learning of tasks, i.e. finding the best order of tasks to be learned. Our approach is based on a generalization bound criterion for choosing the task order that optimizes the average expected classification performance over all tasks. Our experimental results show that learning multiple related tasks sequentially can be more effective than learning them jointly, the order in which tasks are being solved affects the overall performance, and that our model is able to automatically discover the favourable order of tasks.
Face verification remains a challenging problem in very complex conditions with large variations such as pose, illumination, expression, and occlusions. This problem is exacerbated when we rely unrealistically on a single training data source, which is often insufficient to cover the intrinsically complex face variations. This paper proposes a principled multi-task learning approach based on Discriminative Gaussian Process Latent Variable Model, named GaussianFace, to enrich the diversity of training data. In comparison to existing methods, our model exploits additional data from multiple source-domains to improve the generalization performance of face verification in an unknown target-domain. Importantly, our model can adapt automatically to complex data distributions, and therefore can well capture complex face variations inherent in multiple sources. Extensive experiments demonstrate the effectiveness of the proposed model in learning from diverse data sources and generalize to unseen domain. Specifically, the accuracy of our algorithm achieves an impressive accuracy rate of 98.52% on the well-known and challenging Labeled Faces in the Wild (LFW) benchmark. For the first time, the human-level performance in face verification (97.53%) on LFW is surpassed.
In this paper, we provide a new neural-network based perspective on multi-task learning (MTL) and multi-domain learning (MDL). By introducing the concept of a semantic descriptor, this framework unifies MDL and MTL as well as encompassing various classic and recent MTL/MDL algorithms by interpreting them as different ways of constructing semantic descriptors. Our interpretation provides an alternative pipeline for zero-shot learning (ZSL), where a model for a novel class can be constructed without training data. Moreover, it leads to a new and practically relevant problem setting of zero-shot domain adaptation (ZSDA), which is the analogous to ZSL but for novel domains: A model for an unseen domain can be generated by its semantic descriptor. Experiments across this range of problems demonstrate that our framework outperforms a variety of alternatives.
We develop a representation suitable for the unconstrained recognition of words in natural images: the general case of no fixed lexicon and unknown length. To this end we propose a convolutional neural network (CNN) based architecture which incorporates a Conditional Random Field (CRF) graphical model, taking the whole word image as a single input. The unaries of the CRF are provided by a CNN that predicts characters at each position of the output, while higher order terms are provided by another CNN that detects the presence of N-grams. We show that this entire model (CRF, character predictor, N-gram predictor) can be jointly optimised by back-propagating the structured output loss, essentially requiring the system to perform multi-task learning, and training uses purely synthetically generated data. The resulting model is a more accurate system on standard real-world text recognition benchmarks than character prediction alone, setting a benchmark for systems that have not been trained on a particular lexicon. In addition, our model achieves state-of-the-art accuracy in lexicon-constrained scenarios, without being specifically modelled for constrained recognition. To test the generalisation of our model, we also perform experiments with random alpha-numeric strings to evaluate the method when no visual language model is applicable.
Multi-task learning is a natural approach for computer vision applications that require the simultaneous solution of several distinct but related problems, e.g. object detection, classification, tracking of multiple agents, or denoising, to name a few. The key idea is that exploring task relatedness (structure) can lead to improved performances. In this paper, we propose and study a novel sparse, non-parametric approach exploiting the theory of Reproducing Kernel Hilbert Spaces for vector-valued functions. We develop a suitable regularization framework which can be formulated as a convex optimization problem, and is provably solvable using an alternating minimization approach. Empirical tests show that the proposed method compares favorably to state of the art techniques and further allows to recover interpretable structures, a problem of interest in its own right.
Reducing the amount of human supervision is a key problem in machine learning and a natural approach is that of exploiting the relations (structure) among different tasks. This is the idea at the core of multi-task learning. In this context a fundamental question is how to incorporate the tasks structure in the learning problem.We tackle this question by studying a general computational framework that allows to encode a-priori knowledge of the tasks structure in the form of a convex penalty; in this setting a variety of previously proposed methods can be recovered as special cases, including linear and non-linear approaches. Within this framework, we show that tasks and their structure can be efficiently learned considering a convex optimization problem that can be approached by means of block coordinate methods such as alternating minimization and for which we prove convergence to the global minimum.
Additive models form a widely popular class of regression models which represent the relation between covariates and response variables as the sum of low-dimensional transfer functions. Besides flexibility and accuracy, a key benefit of these models is their interpretability: the transfer functions provide visual means for inspecting the models and identifying domain-specific relations between inputs and outputs. However, in large-scale problems involving the prediction of many related tasks, learning independently additive models results in a loss of model interpretability, and can cause overfitting when training data is scarce. We introduce a novel multi-task learning approach which provides a corpus of accurate and interpretable additive models for a large number of related forecasting tasks. Our key idea is to share transfer functions across models in order to reduce the model complexity and ease the exploration of the corpus. We establish a connection with sparse dictionary learning and propose a new efficient fitting algorithm which alternates between sparse coding and transfer function updates. The former step is solved via an extension of Orthogonal Matching Pursuit, whose properties are analyzed using a novel recovery condition which extends existing results in the literature. The latter step is addressed using a traditional dictionary update rule. Experiments on real-world data demonstrate that our approach compares favorably to baseline methods while yielding an interpretable corpus of models, revealing structure among the individual tasks and being more robust when training data is scarce. Our framework therefore extends the well-known benefits of additive models to common regression settings possibly involving thousands of tasks.
We present a general regularization-based framework for Multi-task learning (MTL), in which the similarity between tasks can be learned or refined using $\ell_p$-norm Multiple Kernel learning (MKL). Based on this very general formulation (including a general loss function), we derive the corresponding dual formulation using Fenchel duality applied to Hermitian matrices. We show that numerous established MTL methods can be derived as special cases from both, the primal and dual of our formulation. Furthermore, we derive a modern dual-coordinate descend optimization strategy for the hinge-loss variant of our formulation and provide convergence bounds for our algorithm. As a special case, we implement in C++ a fast LibLinear-style solver for $\ell_p$-norm MKL. In the experimental section, we analyze various aspects of our algorithm such as predictive performance and ability to reconstruct task relationships on biologically inspired synthetic data, where we have full control over the underlying ground truth. We also experiment on a new dataset from the domain of computational biology that we collected for the purpose of this paper. It concerns the prediction of transcription start sites (TSS) over nine organisms, which is a crucial task in gene finding. Our solvers including all discussed special cases are made available as open-source software as part of the SHOGUN machine learning toolbox (available at \url{http://shogun.ml}).
Automatically detecting, labeling, and tracking objects in videos depends first and foremost on accurate category-level object detectors. These might, however, not always be available in practice, as acquiring high-quality large scale labeled training datasets is either too costly or impractical for all possible real-world application scenarios. A scalable solution consists in re-using object detectors pre-trained on generic datasets. This work is the first to investigate the problem of on-line domain adaptation of object detectors for causal multi-object tracking (MOT). We propose to alleviate the dataset bias by adapting detectors from category to instances, and back: (i) we jointly learn all target models by adapting them from the pre-trained one, and (ii) we also adapt the pre-trained model on-line. We introduce an on-line multi-task learning algorithm to efficiently share parameters and reduce drift, while gradually improving recall. Our approach is applicable to any linear object detector, and we evaluate both cheap "mini-Fisher Vectors" and expensive "off-the-shelf" ConvNet features. We quantitatively measure the benefit of our domain adaptation strategy on the KITTI tracking benchmark and on a new dataset (PASCAL-to-KITTI) we introduce to study the domain mismatch problem in MOT.
Log-density gradient estimation is a fundamental statistical problem and possesses various practical applications such as clustering and measuring non-Gaussianity. A naive two-step approach of first estimating the density and then taking its log-gradient is unreliable because an accurate density estimate does not necessarily lead to an accurate log-density gradient estimate. To cope with this problem, a method to directly estimate the log-density gradient without density estimation has been explored, and demonstrated to work much better than the two-step method. The objective of this paper is to further improve the performance of this direct method in multi-dimensional cases. Our idea is to regard the problem of log-density gradient estimation in each dimension as a task, and apply regularized multi-task learning to the direct log-density gradient estimator. We experimentally demonstrate the usefulness of the proposed multi-task method in log-density gradient estimation and mode-seeking clustering.
When faced with learning a set of inter-related tasks from a limited amount of usable data, learning each task independently may lead to poor generalization performance. Multi-Task Learning (MTL) exploits the latent relations between tasks and overcomes data scarcity limitations by co-learning all these tasks simultaneously to offer improved performance. We propose a novel Multi-Task Multiple Kernel Learning framework based on Support Vector Machines for binary classification tasks. By considering pair-wise task affinity in terms of similarity between a pair's respective feature spaces, the new framework, compared to other similar MTL approaches, offers a high degree of flexibility in determining how similar feature spaces should be, as well as which pairs of tasks should share a common feature space in order to benefit overall performance. The associated optimization problem is solved via a block coordinate descent, which employs a consensus-form Alternating Direction Method of Multipliers algorithm to optimize the Multiple Kernel Learning weights and, hence, to determine task affinities. Empirical evaluation on seven data sets exhibits a statistically significant improvement of our framework's results compared to the ones of several other Clustered Multi-Task Learning methods.