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The classical two-sample test of Kolmogorov-Smirnov (KS) is widely used to test whether empirical samples come from the same distribution. Even though most statistical packages provide an implementation, carrying out the test in big data settings can be challenging because it requires a full sort of the data. The popular Apache Spark system for big data processing provides a 1-sample KS test, but not the 2-sample version. Moreover, recent Spark versions provide the approxQuantile method for querying $\epsilon$-approximate quantiles. We build on approxQuantile to propose a variation of the classical Kolmogorov-Smirnov two-sample test that constructs approximate cumulative distribution functions (CDF) from $\epsilon$-approximate quantiles. We derive error bounds of the approximate CDF and show how to use this information to carry out KS tests. Psuedocode for the approach requires 15 executable lines. A Python implementation appears in the appendix.

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 Apache Spark 是專為大規模數據處理而設計的快速通用的計算引擎。Spark是UC Berkeley AMP lab (加州大學伯克利分校的AMP實驗室)所開源的類Hadoop MapReduce的通用并行框架,Spark,擁有Hadoop MapReduce所具有的優點;但不同于MapReduce的是Job中間輸出結果可以保存在內存中,從而不再需要讀寫HDFS,因此Spark能更好地適用于數據挖掘與機器學習等需要迭代的MapReduce的算法。

We propose a novel family of decision-aware surrogate losses, called Perturbation Gradient (PG) losses, for the predict-then-optimize framework. These losses directly approximate the downstream decision loss and can be optimized using off-the-shelf gradient-based methods. Importantly, unlike existing surrogate losses, the approximation error of our PG losses vanishes as the number of samples grows. This implies that optimizing our surrogate loss yields a best-in-class policy asymptotically, even in misspecified settings. This is the first such result in misspecified settings and we provide numerical evidence confirming our PG losses substantively outperform existing proposals when the underlying model is misspecified and the noise is not centrally symmetric. Insofar as misspecification is commonplace in practice -- especially when we might prefer a simpler, more interpretable model -- PG losses offer a novel, theoretically justified, method for computationally tractable decision-aware learning.

Influence Maximization (IM) is a crucial problem in data science. The goal is to find a fixed-size set of highly-influential seed vertices on a network to maximize the influence spread along the edges. While IM is NP-hard on commonly-used diffusion models, a greedy algorithm can achieve $(1-1/e)$-approximation, repeatedly selecting the vertex with the highest marginal gain in influence as the seed. Due to theoretical guarantees, rich literature focuses on improving the performance of the greedy algorithm. To estimate the marginal gain, existing work either runs Monte Carlo (MC) simulations of influence spread or pre-stores hundreds of sketches (usually per-vertex information). However, these approaches can be inefficient in time (MC simulation) or space (storing sketches), preventing the ideas from scaling to today's large-scale graphs. This paper significantly improves the scalability of IM using two key techniques. The first is a sketch-compression technique for the independent cascading model on undirected graphs. It allows combining the simulation and sketching approaches to achieve a time-space tradeoff. The second technique includes new data structures for parallel seed selection. Using our new approaches, we implemented PaC-IM: Parallel and Compressed IM. We compare PaC-IM with state-of-the-art parallel IM systems on a 96-core machine with 1.5TB memory. PaC-IM can process large-scale graphs with up to 900M vertices and 74B edges in about 2 hours. On average across all tested graphs, our uncompressed version is 5--18$\times$ faster and about 1.4$\times$ more space-efficient than existing parallel IM systems. Using compression further saves 3.8$\times$ space with only 70% overhead in time on average.

We propose novel "clustering and conquer" procedures for the parallel large-scale ranking and selection (R&S) problem, which leverage correlation information for clustering to break the bottleneck of sample efficiency. In parallel computing environments, correlation-based clustering can achieve an $\mathcal{O}(p)$ sample complexity reduction rate, which is the optimal reduction rate theoretically attainable. Our proposed framework is versatile, allowing for seamless integration of various prevalent R&S methods under both fixed-budget and fixed-precision paradigms. It can achieve improvements without the necessity of highly accurate correlation estimation and precise clustering. In large-scale AI applications such as neural architecture search, a screening-free version of our procedure surprisingly surpasses fully-sequential benchmarks in terms of sample efficiency. This suggests that leveraging valuable structural information, such as correlation, is a viable path to bypassing the traditional need for screening via pairwise comparison--a step previously deemed essential for high sample efficiency but problematic for parallelization. Additionally, we propose a parallel few-shot clustering algorithm tailored for large-scale problems.

The approach to giving a proof-theoretic semantics for IMLL taken by Gheorghiu, Gu and Pym is an interesting adaptation of the work presented by Sandqvist in his 2015 paper for IPL. What is particularly interesting is how naturally the move to the substructural setting provided a semantics for the multiplicative fragment of intuitionistic linear logic. Whilst ultimately the authors of the semantics for IMLL used their foundations to provide a semantics for bunched implication logic, it begs the question, what of the rest of intuitionistic linear logic? In this paper, I present a semantics for intuitionistic linear logic, by first presenting a semantics for the multiplicative and additive fragment after which we focus solely on considering the modality "of-course", thus giving a proof-theoretic semantics for intuitionistic linear logic.

The Sliced-Wasserstein (SW) distance between probability measures is defined as the average of the Wasserstein distances resulting for the associated one-dimensional projections. As a consequence, the SW distance can be written as an integral with respect to the uniform measure on the sphere and the Monte Carlo framework can be employed for calculating the SW distance. Spherical harmonics are polynomials on the sphere that form an orthonormal basis of the set of square-integrable functions on the sphere. Putting these two facts together, a new Monte Carlo method, hereby referred to as Spherical Harmonics Control Variates (SHCV), is proposed for approximating the SW distance using spherical harmonics as control variates. The resulting approach is shown to have good theoretical properties, e.g., a no-error property for Gaussian measures under a certain form of linear dependency between the variables. Moreover, an improved rate of convergence, compared to Monte Carlo, is established for general measures. The convergence analysis relies on the Lipschitz property associated to the SW integrand. Several numerical experiments demonstrate the superior performance of SHCV against state-of-the-art methods for SW distance computation.

Most existing neural-based text-to-speech methods rely on extensive datasets and face challenges under low-resource condition. In this paper, we introduce a novel semi-supervised text-to-speech synthesis model that learns from both paired and unpaired data to address this challenge. The key component of the proposed model is a dynamic quantized representation module, which is integrated into a sequential autoencoder. When given paired data, the module incorporates a trainable codebook that learns quantized representations under the supervision of the paired data. However, due to the limited paired data in low-resource scenario, these paired data are difficult to cover all phonemes. Then unpaired data is fed to expand the dynamic codebook by adding quantized representation vectors that are sufficiently distant from the existing ones during training. Experiments show that with less than 120 minutes of paired data, the proposed method outperforms existing methods in both subjective and objective metrics.

Despite the predominance of contextualized embeddings in NLP, approaches to detect semantic change relying on these embeddings and clustering methods underperform simpler counterparts based on static word embeddings. This stems from the poor quality of the clustering methods to produce sense clusters -- which struggle to capture word senses, especially those with low frequency. This issue hinders the next step in examining how changes in word senses in one language influence another. To address this issue, we propose a graph-based clustering approach to capture nuanced changes in both high- and low-frequency word senses across time and languages, including the acquisition and loss of these senses over time. Our experimental results show that our approach substantially surpasses previous approaches in the SemEval2020 binary classification task across four languages. Moreover, we showcase the ability of our approach as a versatile visualization tool to detect semantic changes in both intra-language and inter-language setups. We make our code and data publicly available.

To retrieve more relevant, appropriate and useful documents given a query, finding clues about that query through the text is crucial. Recent deep learning models regard the task as a term-level matching problem, which seeks exact or similar query patterns in the document. However, we argue that they are inherently based on local interactions and do not generalise to ubiquitous, non-consecutive contextual relationships.In this work, we propose a novel relevance matching model based on graph neural networks to leverage the document-level word relationships for ad-hoc retrieval. In addition to the local interactions, we explicitly incorporate all contexts of a term through the graph-of-word text format. Matching patterns can be revealed accordingly to provide a more accurate relevance score. Our approach significantly outperforms strong baselines on two ad-hoc benchmarks. We also experimentally compare our model with BERT and show our ad-vantages on long documents.

Recently pre-trained language representation models such as BERT have shown great success when fine-tuned on downstream tasks including information retrieval (IR). However, pre-training objectives tailored for ad-hoc retrieval have not been well explored. In this paper, we propose Pre-training with Representative wOrds Prediction (PROP) for ad-hoc retrieval. PROP is inspired by the classical statistical language model for IR, specifically the query likelihood model, which assumes that the query is generated as the piece of text representative of the "ideal" document. Based on this idea, we construct the representative words prediction (ROP) task for pre-training. Given an input document, we sample a pair of word sets according to the document language model, where the set with higher likelihood is deemed as more representative of the document. We then pre-train the Transformer model to predict the pairwise preference between the two word sets, jointly with the Masked Language Model (MLM) objective. By further fine-tuning on a variety of representative downstream ad-hoc retrieval tasks, PROP achieves significant improvements over baselines without pre-training or with other pre-training methods. We also show that PROP can achieve exciting performance under both the zero- and low-resource IR settings. The code and pre-trained models are available at //github.com/Albert-Ma/PROP.

Most existing works in visual question answering (VQA) are dedicated to improving the accuracy of predicted answers, while disregarding the explanations. We argue that the explanation for an answer is of the same or even more importance compared with the answer itself, since it makes the question and answering process more understandable and traceable. To this end, we propose a new task of VQA-E (VQA with Explanation), where the computational models are required to generate an explanation with the predicted answer. We first construct a new dataset, and then frame the VQA-E problem in a multi-task learning architecture. Our VQA-E dataset is automatically derived from the VQA v2 dataset by intelligently exploiting the available captions. We have conducted a user study to validate the quality of explanations synthesized by our method. We quantitatively show that the additional supervision from explanations can not only produce insightful textual sentences to justify the answers, but also improve the performance of answer prediction. Our model outperforms the state-of-the-art methods by a clear margin on the VQA v2 dataset.

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