The data on user behaviors is sparse given the vast array of user-item combinations. Attributes related to users (e.g., age), items (e.g., brand), and behaviors (e.g., co-purchase) serve as crucial input sources for item-item transitions of user's behavior prediction. While recent Transformer-based sequential recommender systems learn the attention matrix for each attribute to update item representations, the attention of a specific attribute is optimized by gradients from all input sources, leading to potential information mixture. Besides, Transformers mainly focus on intra-sequence attention for item attributes, neglecting cross-sequence relations and user attributes. Addressing these challenges, we propose the Attribute Transformer (AttrFormer) to learn attributes as explicit relations. This model transforms each type of attribute into an explicit relation defined in the feature space, and it ensures no information mixing among different input sources. Explicit relations introduce cross-sequence and intra-sequence relations. AttrFormer has novel relation-augmented heads to handle them at both the item and behavioral levels, seamlessly integrating the augmented heads into the multi-head attention mechanism. Furthermore, we employ position-to-position aggregation to refine behavior representation for users with similar patterns at the sequence level. To capture the subjective nature of user preferences, AttrFormer is trained using posterior targets where upcoming user behaviors follow a multinomial distribution with a Dirichlet prior. Our evaluations on four popular datasets, including Amazon (Toys & Games and Beauty) and MovieLens (1M and 25M versions), reveal that AttrFormer outperforms leading Transformer baselines, achieving around 20% improvement in NDCG@20 scores. Extensive ablation studies also demonstrate the efficiency of AttrFormer in managing long behavior sequences and inter-sequence relations.

We study the performance of kernel methods on the acoustic modeling task for automatic speech recognition, and compare their performance to deep neural networks (DNNs). To scale the kernel methods to large data sets, we use the random Fourier feature method of Rahimi and Recht (2007). We propose two novel techniques for improving the performance of kernel acoustic models. First, we propose a simple but effective feature selection method which reduces the number of random features required to attain a fixed level of performance. Second, we present a number of metrics which correlate strongly with speech recognition performance when computed on the heldout set; we attain improved performance by using these metrics to decide when to stop training. Additionally, we show that the linear bottleneck method of Sainath et al. (2013a) improves the performance of our kernel models significantly, in addition to speeding up training and making the models more compact. Leveraging these three methods, the kernel methods attain token error rates between $0.5\%$ better and $0.1\%$ worse than fully-connected DNNs across four speech recognition data sets, including the TIMIT and Broadcast News benchmark tasks.

We study large-scale kernel methods for acoustic modeling and compare to DNNs on performance metrics related to both acoustic modeling and recognition. Measuring perplexity and frame-level classification accuracy, kernel-based acoustic models are as effective as their DNN counterparts. However, on token-error-rates DNN models can be significantly better. We have discovered that this might be attributed to DNN's unique strength in reducing both the perplexity and the entropy of the predicted posterior probabilities. Motivated by our findings, we propose a new technique, entropy regularized perplexity, for model selection. This technique can noticeably improve the recognition performance of both types of models, and reduces the gap between them. While effective on Broadcast News, this technique could be also applicable to other tasks.

Learning sparse combinations is a frequent theme in machine learning. In this paper, we study its associated optimization problem in the distributed setting where the elements to be combined are not centrally located but spread over a network. We address the key challenges of balancing communication costs and optimization errors. To this end, we propose a distributed Frank-Wolfe (dFW) algorithm. We obtain theoretical guarantees on the optimization error ∊ and communication cost that do not depend on the total number of combining elements. We further show that the communication cost of dFW is optimal by deriving a lowerbound on the communication cost required to construct an ∊-approximate solution. We validate our theoretical analysis with empirical studies on synthetic and real-world data, which demonstrate that dFW outperforms both baselines and competing methods. We also study the performance of dFW when the conditions of our analysis are relaxed, and show that dFW is fairly robust.