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Novel architectures have recently improved generative image synthesis leading to excellent visual quality in various tasks. Much of this success is due to the scalability of these architectures and hence caused by a dramatic increase in model complexity and in the computational resources invested in training these models. Our work questions the underlying paradigm of compressing large training data into ever growing parametric representations. We rather present an orthogonal, semi-parametric approach. We complement comparably small diffusion or autoregressive models with a separate image database and a retrieval strategy. During training we retrieve a set of nearest neighbors from this external database for each training instance and condition the generative model on these informative samples. While the retrieval approach is providing the (local) content, the model is focusing on learning the composition of scenes based on this content. As demonstrated by our experiments, simply swapping the database for one with different contents transfers a trained model post-hoc to a novel domain. The evaluation shows competitive performance on tasks which the generative model has not been trained on, such as class-conditional synthesis, zero-shot stylization or text-to-image synthesis without requiring paired text-image data. With negligible memory and computational overhead for the external database and retrieval we can significantly reduce the parameter count of the generative model and still outperform the state-of-the-art.

A probabilistic secret sharing scheme is a joint probability distribution of the shares and the secret together with a collection of secret recovery functions. The study of schemes using arbitrary probability spaces and unbounded number of participants allows us to investigate their abstract properties, to connect the topic to other branches of mathematics, and to discover new design paradigms. A scheme is perfect if unqualified subsets have no information on the secret, that is, their total share is independent of the secret. By relaxing this security requirement, three other scheme types are defined. Our first result is that every (infinite) access structure can be realized by a perfect scheme where the recovery functions are non-measurable. The construction is based on a paradoxical pair of independent random variables which determine each other. Restricting the recovery functions to be measurable ones, we give a complete characterization of access structures realizable by each type of the schemes. In addition, either a vector-space or a Hilbert-space based scheme is constructed realizing the access structure. While the former one uses the traditional uniform distributions, the latter one uses Gaussian distributions, leading to a new design paradigm.

In some inferential statistical methods, such as tests and confidence intervals, it is important to describe the stochastic behavior of statistical functionals, aside from their large sample properties. We study such behavior in terms of the usual stochastic order. For this purpose, we introduce a generalized family of stochastic orders, which is referred to as transform orders, showing that it provides a flexible framework for deriving stochastic monotonicity results. Given that our general definition makes it possible to obtain some well-known ordering relations as particular cases, we can easily apply our method to different families of functionals. These include some prominent inequality measures, such as the generalized entropy, the Gini index, and its generalizations. We also illustrate the applicability of our approach by determining the least favorable distribution, and the behavior of some bootstrap statistics, in some goodness-of-fit testing procedures.

Wind power forecasting is essential to power system operation and electricity markets. As abundant data became available thanks to the deployment of measurement infrastructures and the democratization of meteorological modelling, extensive data-driven approaches have been developed within both point and probabilistic forecasting frameworks. These models usually assume that the dataset at hand is complete and overlook missing value issues that often occur in practice. In contrast to that common approach, we rigorously consider here the wind power forecasting problem in the presence of missing values, by jointly accommodating imputation and forecasting tasks. Our approach allows inferring the joint distribution of input features and target variables at the model estimation stage based on incomplete observations only. We place emphasis on a fully conditional specification method owing to its desirable properties, e.g., being assumption-free when it comes to these joint distributions. Then, at the operational forecasting stage, with available features at hand, one can issue forecasts by implicitly imputing all missing entries. The approach is applicable to both point and probabilistic forecasting, while yielding competitive forecast quality within both simulation and real-world case studies. It confirms that by using a powerful universal imputation method like fully conditional specification, the proposed approach is superior to the common approach, especially in the context of probabilistic forecasting.

The past several years have witnessed Variational Auto-Encoder's superiority in various text generation tasks. However, due to the sequential nature of the text, auto-regressive decoders tend to ignore latent variables and then reduce to simple language models, known as the KL vanishing problem, which would further deteriorate when VAE is combined with Transformer-based structures. To ameliorate this problem, we propose DELLA, a novel variational Transformer framework. DELLA learns a series of layer-wise latent variables with each inferred from those of lower layers and tightly coupled with the hidden states by low-rank tensor product. In this way, DELLA forces these posterior latent variables to be fused deeply with the whole computation path and hence incorporate more information. We theoretically demonstrate that our method can be regarded as entangling latent variables to avoid posterior information decrease through layers, enabling DELLA to get higher non-zero KL values even without any annealing or thresholding tricks. Experiments on four unconditional and three conditional generation tasks show that DELLA could better alleviate KL vanishing and improve both quality and diversity compared to several strong baselines.

Collecting complete network data is expensive, time-consuming, and often infeasible. Aggregated Relational Data (ARD), which capture information about a social network by asking a respondent questions of the form ``How many people with trait X do you know?'' provide a low-cost option when collecting complete network data is not possible. Rather than asking about connections between each pair of individuals directly, ARD collects the number of contacts the respondent knows with a given trait. Despite widespread use and a growing literature on ARD methodology, there is still no systematic understanding of when and why ARD should accurately recover features of the unobserved network. This paper provides such a characterization by deriving conditions under which statistics about the unobserved network (or functions of these statistics like regression coefficients) can be consistently estimated using ARD. We do this by first providing consistent estimates of network model parameters for three commonly used probabilistic models: the beta-model with node-specific unobserved effects, the stochastic block model with unobserved community structure, and latent geometric space models with unobserved latent locations. A key observation behind these results is that cross-group link probabilities for a collection of (possibly unobserved) groups identifies the model parameters, meaning ARD is sufficient for parameter estimation. With these estimated parameters, it is possible to simulate graphs from the fitted distribution and analyze the distribution of network statistics. We can then characterize conditions under which the simulated networks based on ARD will allow for consistent estimation of the unobserved network statistics, such as eigenvector centrality or response functions by or of the unobserved network, such as regression coefficients.

Keyphrase generation aims at generating important phrases (keyphrases) that best describe a given document. In scholarly domains, current approaches have largely used only the title and abstract of the articles to generate keyphrases. In this paper, we comprehensively explore whether the integration of additional information from the full text of a given article or from semantically similar articles can be helpful for a neural keyphrase generation model or not. We discover that adding sentences from the full text, particularly in the form of the extractive summary of the article can significantly improve the generation of both types of keyphrases that are either present or absent from the text. Experimental results with three widely used models for keyphrase generation along with one of the latest transformer models suitable for longer documents, Longformer Encoder-Decoder (LED) validate the observation. We also present a new large-scale scholarly dataset FullTextKP for keyphrase generation. Unlike prior large-scale datasets, FullTextKP includes the full text of the articles along with the title and abstract. We release the source code at //github.com/kgarg8/FullTextKP.

We show that completeness at higher levels of the theory of the reals is a robust notion (under changing the signature and bounding the domain of the quantifiers). This mends recognized gaps in the hierarchy, and leads to stronger completeness results for various computational problems. We exhibit several families of complete problems which can be used for future completeness results in the real hierarchy. As an application we answer an open question by Jungeblut, Kleist, and Miltzow on the complexity of two semialgebraic sets having Hausdorff distance $0$, and sharpen some results by Burgisser and Cucker.

Search engine has become a fundamental component in various web and mobile applications. Retrieving relevant documents from the massive datasets is challenging for a search engine system, especially when faced with verbose or tail queries. In this paper, we explore a vector space search framework for document retrieval. Specifically, we trained a deep semantic matching model so that each query and document can be encoded as a low dimensional embedding. Our model was trained based on BERT architecture. We deployed a fast k-nearest-neighbor index service for online serving. Both offline and online metrics demonstrate that our method improved retrieval performance and search quality considerably, particularly for tail

Pre-trained deep neural network language models such as ELMo, GPT, BERT and XLNet have recently achieved state-of-the-art performance on a variety of language understanding tasks. However, their size makes them impractical for a number of scenarios, especially on mobile and edge devices. In particular, the input word embedding matrix accounts for a significant proportion of the model's memory footprint, due to the large input vocabulary and embedding dimensions. Knowledge distillation techniques have had success at compressing large neural network models, but they are ineffective at yielding student models with vocabularies different from the original teacher models. We introduce a novel knowledge distillation technique for training a student model with a significantly smaller vocabulary as well as lower embedding and hidden state dimensions. Specifically, we employ a dual-training mechanism that trains the teacher and student models simultaneously to obtain optimal word embeddings for the student vocabulary. We combine this approach with learning shared projection matrices that transfer layer-wise knowledge from the teacher model to the student model. Our method is able to compress the BERT_BASE model by more than 60x, with only a minor drop in downstream task metrics, resulting in a language model with a footprint of under 7MB. Experimental results also demonstrate higher compression efficiency and accuracy when compared with other state-of-the-art compression techniques.