Consider the communication-constrained problem of nonpar ametric function estimation, in which each distributed terminal holds multiple i.i.d. Under certain regu larity assumptions, we characterize the minimax optimal rates for all regimes, and identify phase transitions of the optimal rates as the samples per terminal vary from sparse to dense. This fully solves the problem left open by previous works, whose scopes are limited to regimes with either dense samples or a single sample per terminal. To achieve the optimal rates, we design a layered estimation protocol by exploiting protocols for the parametric density estimat ion problem. We show the optimality of the protocol using information-theoretic methods and strong data processing inequalities, and incorporating the classic balls and bins model. The optimal rates are immediate for various special c ases such as density estimation, Gaussian, binary, Poisson and heteroskedastic regression models. Distributed nonparametric estimation problems have attra cted wide attention, and related theoretical studies can shed light on the understanding of modern applications such as federated learning [1], [2], [3].

Consider the communication-constrained estimation of discrete distributions under $\ell^p$ losses, where each distributed terminal holds multiple independent samples and uses limited number of bits to describe the samples. We obtain the minimax optimal rates of the problem in most parameter regimes. An elbow effect of the optimal rates at $p=2$ is clearly identified. To show the optimal rates, we first design estimation protocols to achieve them. The key ingredient of these protocols is to introduce adaptive refinement mechanisms, which first generate rough estimate by partial information and then establish refined estimate in subsequent steps guided by the rough estimate. The protocols leverage successive refinement, sample compression, thresholding and random hashing methods to achieve the optimal rates in different parameter regimes. The optimality of the protocols is shown by deriving compatible minimax lower bounds.

With the rapid development of artificial intelligence, conversational bots have became prevalent in mainstream E-commerce platforms, which can provide convenient customer service timely. To satisfy the user, the conversational bots need to understand the user's intention, detect the user's emotion, and extract the key entities from the conversational utterances. However, understanding dialogues is regarded as a very challenging task. Different from common language understanding, utterances in dialogues appear alternately from different roles and are usually organized as hierarchical structures. To facilitate the understanding of dialogues, in this paper, we propose a novel contextual dialogue encoder (i.e. DialogueBERT) based on the popular pre-trained language model BERT. Five self-supervised learning pre-training tasks are devised for learning the particularity of dialouge utterances. Four different input embeddings are integrated to catch the relationship between utterances, including turn embedding, role embedding, token embedding and position embedding. DialogueBERT was pre-trained with 70 million dialogues in real scenario, and then fine-tuned in three different downstream dialogue understanding tasks. Experimental results show that DialogueBERT achieves exciting results with 88.63% accuracy for intent recognition, 94.25% accuracy for emotion recognition and 97.04% F1 score for named entity recognition, which outperforms several strong baselines by a large margin.

Affinity propagation clustering (AP) has two limitations: it is hard to know what value of parameter 'preference' can yield an optimal clustering solution, and oscillations cannot be eliminated automatically if occur. The adaptive AP method is proposed to overcome these limitations, including adaptive scanning of preferences to search space of the number of clusters for finding the optimal clustering solution, adaptive adjustment of damping factors to eliminate oscillations, and adaptive escaping from oscillations when the damping adjustment technique fails. Experimental results on simulated and real data sets show that the adaptive AP is effective and can outperform AP in quality of clustering results.