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This paper revisits building machine learning algorithms that involve interactions between entities, such as those between financial assets in an actively managed portfolio, or interac- tions between users in a social network. Our goal is to forecast the future evolution of ensembles of multivariate time series in such applications (e.g., the future return of a financial asset or the future popularity of a Twitter account). Designing ML algorithms for such systems requires addressing the challenges of high-dimensional interactions and non-linearity. Existing approaches usually adopt an ad-hoc approach to integrating high-dimensional techniques into non-linear models and re- cent studies have shown these approaches have questionable efficacy in time-evolving interacting systems. To this end, we propose a novel framework, which we dub as the additive influence model. Under our modeling assump- tion, we show that it is possible to decouple the learning of high-dimensional interactions from the learning of non-linear feature interactions. To learn the high-dimensional interac- tions, we leverage kernel-based techniques, with provable guarantees, to embed the entities in a low-dimensional latent space. To learn the non-linear feature-response interactions, we generalize prominent machine learning techniques, includ- ing designing a new statistically sound non-parametric method and an ensemble learning algorithm optimized for vector re- gressions. Extensive experiments on two common applica- tions demonstrate that our new algorithms deliver significantly stronger forecasting power compared to standard and recently proposed methods. 

We study the low rank regression problem $\my = M\mx + \epsilon$, where $\mx$ and $\my$ are d1 and d2 dimensional vectors respectively. We consider the extreme high-dimensional setting where the number of observations n is less than d1+d2. Existing algorithms are designed for settings where n is typically as large as $\Rank(M)(d_1+d_2)$. This work provides an efficient algorithm which only involves two SVD, and establishes statistical guarantees on its performance. The algorithm decouples the problem by first estimating the precision matrix of the features, and then solving the matrix denoising problem. To complement the upper bound, we introduce new techniques for establishing lower bounds on the performance of any algorithm for this problem. Our preliminary experiments confirm that our algorithm often out-performs existing baselines, and is always at least competitive. 

Efficient construction of checkpoints/snapshots is a critical tool for training and diagnosing deep learning models. In this paper, we propose a lossy compression scheme for checkpoint constructions (called LC-Checkpoint). LC-Checkpoint simultaneously maximizes the compression rate and optimizes the recovery speed, under the assumption that SGD is used to train the model. LC-Checkpointuses quantization and priority promotion to store the most crucial information for SGD to recover, and then uses a Huffman coding to leverage the non-uniform distribution of the gradient scales. Our extensive experiments show that LC-Checkpoint achieves a compression rate up to 28× and recovery speedup up to 5.77× over a state-of-the-art algorithm (SCAR).