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Register a new userModel Reuse with Reduced Kernel Mean Embedding Specification
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Given a publicly available pool of machine learning models constructed for various tasks, when a user plans to build a model for her own machine learning application, is it possible to build upon models in the pool such that the previous efforts on these existing models can be reused rather than starting from scratch? Here, a grand challenge is how to find models that are helpful for the current application, without accessing the raw training data for the models in the pool. In this paper, we present a two-phase framework. In the upload phase, when a model is uploading into the pool, we construct a reduced kernel mean embedding (RKME) as a specification for the model. Then in the deployment phase, the relatedness of the current task and pre-trained models will be measured based on the value of the RKME specification. Theoretical results and extensive experiments validate the effectiveness of our approach.
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Estimating the kernel mean in a reproducing kernel Hilbert space is a critical component in many kernel learning algorithms. Given a finite sample, the standard estimate of the target kernel mean is the empirical average. Previous works have shown that better estimators can be constructed by shrinkage methods. In this work, we propose to corrupt data examples with noise from known distributions and present a new kernel mean estimator, called the marginalized kernel mean estimator, which estimates kernel mean under the corrupted distribution. Theoretically, we show that the marginalized kernel mean estimator introduces implicit regularization in kernel mean estimation. Empirically, we show on a variety of datasets that the marginalized kernel mean estimator obtains much lower estimation error than the existing estimators.
The objective in statistical Optimal Transport (OT) is to consistently estimate the optimal transport plan/map solely using samples from the given source and target marginal distributions. This work takes the novel approach of posing statistical OT as that of learning the transport plans kernel mean embedding from sample based estimates of marginal embeddings. The proposed estimator controls overfitting by employing maximum mean discrepancy based regularization, which is complementary to $phi$-divergence (entropy) based regularization popularly employed in existing estimators. A key result is that, under very mild conditions, $epsilon$-optimal recovery of the transport plan as well as the Barycentric-projection based transport map is possible with a sample complexity that is completely dimension-free. Moreover, the implicit smoothing in the kernel mean embeddings enables out-of-sample estimation. An appropriate representer theorem is proved leading to a kernelized convex formulation for the estimator, which can then be potentially used to perform OT even in non-standard domains. Empirical results illustrate the efficacy of the proposed approach.
Graph kernels are widely used for measuring the similarity between graphs. Many existing graph kernels, which focus on local patterns within graphs rather than their global properties, suffer from significant structure information loss when representing graphs. Some recent global graph kernels, which utilizes the alignment of geometric node embeddings of graphs, yield state-of-the-art performance. However, these graph kernels are not necessarily positive-definite. More importantly, computing the graph kernel matrix will have at least quadratic {time} complexity in terms of the number and the size of the graphs. In this paper, we propose a new family of global alignment graph kernels, which take into account the global properties of graphs by using geometric node embeddings and an associated node transportation based on earth movers distance. Compared to existing global kernels, the proposed kernel is positive-definite. Our graph kernel is obtained by defining a distribution over emph{random graphs}, which can naturally yield random feature approximations. The random feature approximations lead to our graph embeddings, which is named as random graph embeddings (RGE). In particular, RGE is shown to achieve emph{(quasi-)linear scalability} with respect to the number and the size of the graphs. The experimental results on nine benchmark datasets demonstrate that RGE outperforms or matches twelve state-of-the-art graph classification algorithms.
Kernel mean embeddings are a popular tool that consists in representing probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. When the kernel is characteristic, mean embeddings can be used to define a distance between probability measures, known as the maximum mean discrepancy (MMD). A well-known advantage of mean embeddings and MMD is their low computational cost and low sample complexity. However, kernel mean embeddings have had limited applications to problems that consist in optimizing distributions, due to the difficulty of characterizing which Hilbert space vectors correspond to a probability distribution. In this note, we propose to leverage the kernel sums-of-squares parameterization of positive functions of Marteau-Ferey et al. [2020] to fit distributions in the MMD geometry. First, we show that when the kernel is characteristic, distributions with a kernel sum-of-squares density are dense. Then, we provide algorithms to optimize such distributions in the finite-sample setting, which we illustrate in a density fitting numerical experiment.
Experience reuse is key to sample-efficient reinforcement learning. One of the critical issues is how the experience is represented and stored. Previously, the experience can be stored in the forms of features, individual models, and the average model, each lying at a different granularity. However, new tasks may require experience across multiple granularities. In this paper, we propose the policy residual representation (PRR) network, which can extract and store multiple levels of experience. PRR network is trained on a set of tasks with a multi-level architecture, where a module in each level corresponds to a subset of the tasks. Therefore, the PRR network represents the experience in a spectrum-like way. When training on a new task, PRR can provide different levels of experience for accelerating the learning. We experiment with the PRR network on a set of grid world navigation tasks, locomotion tasks, and fighting tasks in a video game. The results show that the PRR network leads to better reuse of experience and thus outperforms some state-of-the-art approaches.
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