Yifan Sun

Baojian Zhou, Yifan Sun

In this paper, we consider approximate Frank-Wolfe (FW) algorithms to solve convex optimization problems over graph-structured support sets where the linear minimization oracle (LMO) cannot be efficiently obtained in general. We first demonstrate that two popular approximation assumptions (additive and multiplicative gap errors) are not applicable in that no cheap gap-approximate LMO oracle exists. Thus, approximate dual maximization oracles (DMO) are proposed, which approximate the inner product rather than the gap. We prove that the standard FW method using a $δ$-approximate DMO converges as $\mathcal{O}((1-δ) \sqrt{s}/δ)$ in the worst case, and as $\mathcal{O}(L/(δ^2 t))$ over a $δ$-relaxation of the constraint set. Furthermore, when the solution is on the boundary, a variant of FW converges as $\mathcal{O}(1/t^2)$ under the quadratic growth assumption. Our empirical results suggest that even these improved bounds are pessimistic, showing fast convergence in recovering real-world images with graph-structured sparsity.

Xiangyu Niu, Yifan Sun, Jinyuan Sun

In multi-task learning (MTL), we improve the performance of key machine learning algorithms by training various tasks jointly. When the number of tasks is large, modeling task structure can further refine the task relationship model. For example, often tasks can be grouped based on metadata, or via simple preprocessing steps like K-means. In this paper, we present our group structured latent-space multi-task learning model, which encourages group structured tasks defined by prior information. We use an alternating minimization method to learn the model parameters. Experiments are conducted on both synthetic and real-world datasets, showing competitive performance over single-task learning (where each group is trained separately) and other MTL baselines.

Yifan Sun, Francis Bach

The conditional gradient method (CGM) has been widely used for fast sparse approximation, having a low per iteration computational cost for structured sparse regularizers. We explore the sparsity acquiring properties of a generalized CGM (gCGM), where the constraint is replaced by a penalty function based on a gauge penalty; this can be done without significantly increasing the per-iteration computation, and applies to general notions of sparsity. Without assuming bounded iterates, we show $O(1/t)$ convergence of the function values and gap of gCGM. We couple this with a safe screening rule, and show that at a rate $O(1/(tδ^2))$, the screened support matches the support at the solution, where $δ\geq 0$ measures how close the problem is to being degenerate. In our experiments, we show that the gCGM for these modified penalties have similar feature selection properties as common penalties, but with potentially more stability over the choice of hyperparameter.

Can Karakus, Yifan Sun, Suhas Diggavi et al.

Performance of distributed optimization and learning systems is bottlenecked by "straggler" nodes and slow communication links, which significantly delay computation. We propose a distributed optimization framework where the dataset is "encoded" to have an over-complete representation with built-in redundancy, and the straggling nodes in the system are dynamically left out of the computation at every iteration, whose loss is compensated by the embedded redundancy. We show that oblivious application of several popular optimization algorithms on encoded data, including gradient descent, L-BFGS, proximal gradient under data parallelism, and coordinate descent under model parallelism, converge to either approximate or exact solutions of the original problem when stragglers are treated as erasures. These convergence results are deterministic, i.e., they establish sample path convergence for arbitrary sequences of delay patterns or distributions on the nodes, and are independent of the tail behavior of the delay distribution. We demonstrate that equiangular tight frames have desirable properties as encoding matrices, and propose efficient mechanisms for encoding large-scale data. We implement the proposed technique on Amazon EC2 clusters, and demonstrate its performance over several learning problems, including matrix factorization, LASSO, ridge regression and logistic regression, and compare the proposed method with uncoded, asynchronous, and data replication strategies.

Can Karakus, Yifan Sun, Suhas Diggavi et al.

Slow running or straggler tasks can significantly reduce computation speed in distributed computation. Recently, coding-theory-inspired approaches have been applied to mitigate the effect of straggling, through embedding redundancy in certain linear computational steps of the optimization algorithm, thus completing the computation without waiting for the stragglers. In this paper, we propose an alternate approach where we embed the redundancy directly in the data itself, and allow the computation to proceed completely oblivious to encoding. We propose several encoding schemes, and demonstrate that popular batch algorithms, such as gradient descent and L-BFGS, applied in a coding-oblivious manner, deterministically achieve sample path linear convergence to an approximate solution of the original problem, using an arbitrarily varying subset of the nodes at each iteration. Moreover, this approximation can be controlled by the amount of redundancy and the number of nodes used in each iteration. We provide experimental results demonstrating the advantage of the approach over uncoded and data replication strategies.

Yifan Sun, Nikhil Rao, Weicong Ding

Many NLP applications require disambiguating polysemous words. Existing methods that learn polysemous word vector representations involve first detecting various senses and optimizing the sense-specific embeddings separately, which are invariably more involved than single sense learning methods such as word2vec. Evaluating these methods is also problematic, as rigorous quantitative evaluations in this space is limited, especially when compared with single-sense embeddings. In this paper, we propose a simple method to learn a word representation, given any context. Our method only requires learning the usual single sense representation, and coefficients that can be learnt via a single pass over the data. We propose several new test sets for evaluating word sense induction, relevance detection, and contextual word similarity, significantly supplementing the currently available tests. Results on these and other tests show that while our method is embarrassingly simple, it achieves excellent results when compared to the state of the art models for unsupervised polysemous word representation learning.