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Greedy coordinate descent (GCD) is an efficient optimization algorithm for a wide range of machine learning and data mining applications. GCD could be significantly faster than randomized coordinate descent (RCD) if they have similar per iteration cost. Nevertheless, in some cases, the greedy rule used in GCD cannot be efficiently implemented, leading to huge per iteration cost and making GCD slower than RCD. To alleviate the cost per iteration, the existing solutions rely on maximum inner product search (MIPS) as an approximate greedy rule. But it has been empirically shown that GCD with approximate greedy rule could suffer from slow convergence even with the state-of-the-art MIPS algorithms. We propose a hybrid coordinate descent algorithm with a simple variable partition strategy to tackle the cases when greedy rule cannot be implemented efficiently. The convergence rate and theoretical properties of the new algorithm are presented. The proposed method is shown to be especially useful when the data matrix has a group structure. Numerical experiments with both synthetic and real-world data demonstrate that our new algorithm is competitive against RCD, GCD, approximate GCD with MIPS and their accelerated variants.

UAI 2021

Efficient Greedy Coordinate Descent via Variable Partitioning

convergence analysis

coordinate descent

optimization

The Conference on Uncertainty in Artificial Intelligence (UAI) is one of the premier international conferences on research related to knowledge representation, learning, and reasoning in the presence of uncertainty. It is supported by the [Association for Uncertainty in Artificial Intelligence (AUAI).](https://www.auai.org/)

The 37th Conference on Uncertainty in Artificial Intelligence (UAI 2021) is held fully online. We have an exciting program consisting of keynote talks by [Susan Murphy](https://www.auai.org/uai2021/program?block=A), [Eric Horvitz](https://www.auai.org/uai2021/program?block=B), [Lenka Zdeborová](https://www.auai.org/uai2021/program?block=C), [Judea Pearl](https://www.auai.org/uai2021/program?block=D) and [Ankur Moitra](https://www.auai.org/uai2021/program?block=E), a town hall meeting, peer-reviewed papers, and three workshops. The main conference is single-track and each paper is show-cased with a live component (either a live discussion and Q&A, or a live lightning talk). All papers are also featured in video presentations and in poster sessions in gather.town. The three parallel workshops on Friday allow for smaller meetings on current topics.

The walkthrough video below shows how you can navigate this site and use the different possibilities for interaction: UAIsland2021 on gather.town for posters and social interactions, the mementor platform for virtual mentoring sessions, and the chat and Q&A systems for discussions about talks and posters.

Have a great UAI 2021! 
<br>
<br>Cassio de Campos and Marloes Maathuis
<br>UAI 2021 Program Chairs
<br>uai2021programchairs@gmail.com

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A ticket is required to access this conference. Please use the provided link to register for the event.

https://auai.org/uai2021/registration

The Conference on Uncertainty in Artificial Intelligence (UAI) is one of the premier international conferences on research related to knowledge representation, learning, and reasoning in the presence of uncertainty. It is supported by the [Association for Uncertainty in Artificial Intelligence (AUAI).](https://www.auai.org/)

Naval Information Warfare Center Pacific is partnering with AFCEA San Diego chapter to host the workshop.

The NAML workshop is an opportunity for researchers from Navy research and development centers and our partner organizations to exchange technical ideas and to come together as a team.

The goals of NAML are:

* To spread awareness of current machine learning research relevant to Naval applications

* To connect machine learning researchers with experts in military requirements

* To build and strengthen collaborations within the defense research community

**Watch this video to hear about the AFCEA purpose.**

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NAML 2021

lightning talk

Multi-source domain adaptation (DA) is more challenging than conventional DA because the knowledge is transferred from several source domains to a target domain. To this end, we propose in this paper a novel model for multi-source DA using the theory of optimal transport and imitation learning. More specifically, our approach consists of two cooperative agents: a teacher classifier and a student classifier. The teacher classifier is a combined expert that leverages knowledge of domain experts that can be theoretically guaranteed to handle perfectly source examples, while the student classifier acting on the target domain tries to imitate the teacher classifier acting on the source domains. Our rigorous theory developed based on optimal transport makes this cross-domain imitation possible and also helps to mitigate not only the data shift but also the label shift, which are inherently thorny issues in DA research. We conduct comprehensive experiments on real-world datasets to demonstrate the merit of our approach and its optimal transport based imitation learning viewpoint. Experimental results show that our proposed method achieves state-of-the-art performance on benchmark datasets for multi-source domain adaptation including Digits-five, Office-Caltech10, and Office-31 to the best of our knowledge.

Multi-Source Domain Adaptation via Optimal Transport for Student-Teacher Learning

Adversarial machine learning has attracted a great amount of attention in recent years.

Defending SVMs Against Poisoning Attacks: The Hardness and DBSCAN Approach

We present a novel blind source separation (BSS) method, called information geometric blind source separation (IGBSS). Our formulation is based on the log-linear model equipped with a hierarchically structured sample space, which has theoretical guarantees to uniquely recover a set of source signals by minimizing the KL divergence from a set of mixed signals. Source signals, received signals, and mixing matrices are realized as different layers in our hierarchical sample space. Our empirical results have demonstrated on images and time series data that our approach is superior to well established techniques and is able to separate signals with complex interactions.

Hierarchical Probabilistic Model for Blind Source Separation via Legendre Transformation

Leveraging the framework of Optimal Transport, we introduce a new family of generative autoencoders with a learnable prior, called Symmetric Wasserstein Autoencoders (SWAEs). We propose to symmetrically match the joint distributions of the observed data and the latent representation induced by the encoder and the decoder. The resulting algorithm jointly optimizes the modelling losses in both the data and the latent spaces with the loss in the data space leading to the denoising effect. With the symmetric treatment of the data and the latent representation, the algorithm implicitly preserves the local structure of the data in the latent space.

Symmetric Wasserstein Autoencoders

Adaptive gradient methods have achieved remarkable success in training deep neural networks on a wide variety of tasks. However, not much is known about the mathematical and statistical properties of this family of methods. This work aims at providing a series of theoretical analyses of its statistical properties justified by experiments. In particular, we show that when the underlying gradient obeys a normal distribution, the variance of the magnitude of the \textit{update} is an increasing and bounded function of time and does not diverge. This work suggests that the divergence of variance is not the cause of the need for warm-up of the Adam optimizer, contrary to what is believed in the current literature.

On the Distributional Properties of Adaptive Gradients

Recent advances in convolutional neural networks (CNNs) usually come with the expense of excessive computational overhead and memory footprint. Network compression aims to alleviate this issue by training compact models with comparable performance. However, existing compression techniques either entail dedicated expert design or compromise with a moderate performance drop. In this paper, we propose a novel structured sparsification method for efficient network compression. The proposed method automatically induces structured sparsity on the convolutional weights, thereby facilitating the implementation of the compressed model with the highly-optimized group convolution. We further address the problem of inter-group communication with a learnable channel shuffle mechanism. The proposed approach can be easily applied to compress many network architectures with a negligible performance drop. Extensive experimental results and analysis demonstrate that our approach gives a competitive performance against the recent network compression counterparts with a sound accuracy-complexity trade-off.

Structured Sparsification with Joint Optimization of Group Convolution and Channel Shuffle

This paper studies the complexity for finding approximate stationary points of nonconvex-strongly-concave (NC-SC) smooth minimax problems, in both general and averaged smooth finite-sum settings. We establish nontrivial lower complexity bounds of $\Omega(\sqrt{\kappa}\Delta L\epsilon^{-2})$ and $\Omega(n+\sqrt{n\kappa}\Delta L\epsilon^{-2})$ for the two settings, respectively, where $\kappa$ is the condition number, $L$ is the smoothness constant, and $\Delta$ is the initial gap. Our result reveals substantial gaps between these limits and best-known upper bounds in the literature. To close these gaps, we introduce a generic acceleration scheme that deploys existing gradient-based methods to solve a sequence of crafted strongly-convex-strongly-concave subproblems. In the general setting, the complexity of our proposed algorithm nearly matches the lower bound; in particular, it removes an additional poly-logarithmic dependence on accuracy present in previous works. In the averaged smooth finite-sum setting, our proposed algorithm improves over previous algorithms by providing a nearly-tight dependence on the condition number.

The Complexity of Nonconvex-Strongly-Concave Minimax Optimization

Bayesian optimization (BO) is a powerful paradigm for efficient optimization of black-box objective functions. High-dimensional BO presents a particular challenge, in part because the curse of dimensionality makes it difficult to define---as well as do inference over---a suitable class of surrogate models. We argue that Gaussian process surrogate models defined on sparse axis-aligned subspaces offer an attractive compromise between flexibility and parsimony. We demonstrate that our approach, which relies on Hamiltonian Monte Carlo for inference, can rapidly identify sparse subspaces relevant to modeling the unknown objective function, enabling sample-efficient high-dimensional BO. In an extensive suite of experiments comparing to existing methods for high-dimensional BO we demonstrate that our algorithm, Sparse Axis-Aligned Subspace BO (SAASBO), achieves excellent performance on several synthetic and real-world problems without the need to set problem-specific hyperparameters.

 High-Dimensional Bayesian Optimization with Sparse Axis-Aligned Subspaces

Convex clustering has drawn recent attention because of its competitive performance and nice property to guarantee global optimality. However, convex clustering is infeasible due to its high computational cost for large-scale data sets. We propose a novel method to solve the L1 fusion convex clustering problem by dynamic programming. We develop the Convex clustering Path Algorithm In Near-linear Time (C-PAINT) algorithm to construct the solution path efficiently. The proposed C-PAINT yields the exact solution while other general solvers for convex problems applied in the convex clustering depend on tuning parameters such as step size and threshold, and it usually takes many iterations to converge. Including a sorting process that almost takes no time in practice, the main part of the algorithm takes only linear time. Thus, C-PAINT has superior scalability comparing to other state-of-art algorithms. Moreover, C-PAINT enables the path visualization of clustering solutions for large data. In particular, experiments show our proposed method can solve the convex clustering with 10^7 data points in two minutes. We demonstrate the proposed method using both synthetic data and real data. Our algorithms are implemented in the dpcc R package.

Dynamic visualization for L1 fusion convex clustering in near-linear time

Auto-Encoder (AE) based neural generative frameworks model the joint-distribution between the data and the latent space using an Encoder-Decoder pair, with regularization imposed in terms of a prior over the latent space. Despite their advantages, such as stability in training, efficient inference, the performance of AE based models has not reached the superior standards of the other generative models such as Generative Adversarial Networks (GANs). Motivated by this, we examine the effect of the latent prior on the generation quality of deterministic AE models in this paper. Specifically, we consider the class of Generative AE models with deterministic Encoder-Decoder pair (such as Wasserstein Auto-Encoder (WAE), Adversarial Auto-Encoder (AAE)), and show that having a fixed prior distribution, \textit{a priori}, oblivious to the dimensionality of the `true' latent space, will lead to the infeasibility of the optimization problem considered. As a remedy to the issue mentioned above, we introduce an additional state space in the form of flexibly learnable latent priors, in the optimization objective of WAE/AAE. Additionally, we employ a latent-space interpolation based smoothing scheme to address the non-smoothness that may arise from highly flexible priors. We show the efficacy of our proposed models, called FlexAE and FlexAE-SR, through several experiments on multiple datasets, and demonstrate that FlexAE-SR is the new state-of-the-art for the AE based generative models in terms of generation quality as measured by several metrics such as Fr\'echet Inception Distance, Precision/Recall score. Code for our paper is available at: \url{https://github.com/dair-iitd/FlexAE}

Efficient Greedy Coordinate Descent via Variable Partitioning

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Efficient Greedy Coordinate Descent via Variable Partitioning

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Next from UAI 2021

Multi-Source Domain Adaptation via Optimal Transport for Student-Teacher Learning

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Using Quantum-inspired Algorithms to Solve Optimization Problems

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RESOURCES

Downloads