Weighted sampling is a fundamental tool in data analysis and machine learning pipelines. Samples are used for efficient estimation of statistics or as sparse representations of the data. When weight distributions are skewed, as is often the case in practice, without-replacement (WOR) sampling is much more effective than with-replacement (WR) sampling: it provides a broader representation and higher accuracy for the same number of samples. We design novel composable sketches for WOR $\ell_p$ sampling, weighted sampling of keys according to a power $p\in[0,2]$ of their frequency (or for signed data, sum of updates). Our sketches have size that grows only linearly with the sample size. Our design is simple and practical, despite intricate analysis, and based on off-the-shelf use of widely implemented heavy hitters sketches such as CountSketch. Our method is the first to provide WOR sampling in the important regime of $p>1$ and the first to handle signed updates for $p>0$.
RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能项目中心）
Recently, randomly mapping vectorial data to strings of discrete symbols (i.e., sketches) for fast and space-efficient similarity searches has become popular. Such random mapping is called similarity-preserving hashing and approximates a similarity metric by using the Hamming distance. Although many efficient similarity searches have been proposed, most of them are designed for binary sketches. Similarity searches on integer sketches are in their infancy. In this paper, we present a novel space-efficient trie named $b$-bit sketch trie on integer sketches for scalable similarity searches by lev…
University of Toronto（多伦多大学）；Vector Institute（向量研究所）；CIFAR（加拿大高等研究院）
Sketch drawings capture the salient information of visual concepts. Previous work has shown that neural networks are capable of producing sketches of natural objects drawn from a small number of classes. While earlier approaches focus on generation quality or retrieval, we explore properties of image representations learned by training a model to produce sketches of images. We show that this generative, class-agnostic model produces informative embeddings of images from novel examples, classes, and even novel datasets in a few-shot setting. Additionally, we find that these learned representati…
Sampling is a fundamental technique, and sampling without replacement is often desirable when duplicate samples are not beneficial. Within machine learning, sampling is useful for generating diverse outputs from a trained model. We present an elegant procedure for sampling without replacement from a broad class of randomized programs, including generative neural models that construct outputs sequentially. Our procedure is efficient even for exponentially-large output spaces. Unlike prior work, our approach is incremental, i.e., samples can be drawn one at a time, allowing for increased flexibi…
MIT CSAIL（麻省理工学院计算机科学与人工智能实验室）；ShanghaiTech University（上海科技大学）；Shanghai Jiao Tong University（上海交通大学）；Google Research（谷歌研究院）
3D object reconstruction from a single image is a highly under-determined problem, requiring strong prior knowledge of plausible 3D shapes. This introduces challenges for learning-based approaches, as 3D object annotations are scarce in real images. Previous work chose to train on synthetic data with ground truth 3D information, but suffered from domain adaptation when tested on real data. In this work, we propose MarrNet, an end-to-end trainable model that sequentially estimates 2.5D sketches and 3D object shape. Our disentangled, two-step formulation has three advantages. First, compared to …
School of Computer Science and Engineering, Nanyang Technological University（南洋理工大学计算机科学与工程学院）
Learning meaningful representations of free-hand sketches remains a challenging task given the signal sparsity and the high-level abstraction of sketches. Existing techniques have focused on exploiting either the static nature of sketches with Convolutional Neural Networks (CNNs) or the temporal sequential property with Recurrent Neural Networks (RNNs). In this work, we propose a new representation of sketches as multiple sparsely connected graphs. We design a novel Graph Neural Network (GNN), the Multi-Graph Transformer (MGT), for learning representations of sketches from multiple graphs whic…
Kernel density estimation is a simple and effective method that lies at the heart of many important machine learning applications. Unfortunately, kernel methods scale poorly for large, high dimensional datasets. Approximate kernel density estimation has a prohibitively high memory and computation cost, especially in the streaming setting. Recent sampling algorithms for high dimensional densities can reduce the computation cost but cannot operate online, while streaming algorithms cannot handle high dimensional datasets due to the curse of dimensionality. We propose RACE, an efficient sketching…
For solving finite-sum optimization problems, SGD without replacement sampling is empirically shown to outperform SGD. Denoting by $n$ the number of components in the cost and $K$ the number of epochs of the algorithm , several recent works have shown convergence rates of without-replacement SGD that have better dependency on $n$ and $K$ than the baseline rate of $O(1/(nK))$ for SGD. However, there are two main limitations shared among those works: the rates have extra poly-logarithmic factors on $nK$, and denoting by $κ$ the condition number of the problem, the rates hold after $κ^c\log(nK)$ …
Time series data can be subject to changes in the underlying process that generates them and, because of these changes, models built on old samples can become obsolete or perform poorly. In this work, we present a way to incorporate information about the current data distribution and its evolution across time into machine learning algorithms. Our solution is based on efficiently maintaining statistics, particularly the mean and the variance, of data features at different time resolutions. These data summarisations can be performed over the input attributes, in which case they can then be fed i…
University of Notre Dame（圣母大学）；Lawrence-Livermore Nat’l Lab.（劳伦斯利弗莫尔国家实验室）
Context-free graph grammars have shown a remarkable ability to model structures in real-world relational data. However, graph grammars lack the ability to capture time-changing phenomena since the left-to-right transitions of a production rule do not represent temporal change. In the present work, we describe dynamic vertex-replacement grammars (DyVeRG), which generalize vertex replacement grammars in the time domain by providing a formal framework for updating a learned graph grammar in accordance with modifications to its underlying data. We show that DyVeRG grammars can be learned from, and…
Indraprastha Institute of Information Technology (IIIT-Delhi)（德里信息技术学院）；Indian Institute of Technology, Mandi（印度理工学院曼迪分校）
Categorical attributes are those that can take a discrete set of values, e.g., colours. This work is about compressing vectors over categorical attributes to low-dimension discrete vectors. The current hash-based methods compressing vectors over categorical attributes to low-dimension discrete vectors do not provide any guarantee on the Hamming distances between the compressed representations. Here we present FSketch to create sketches for sparse categorical data and an estimator to estimate the pairwise Hamming distances among the uncompressed data only from their sketches. We claim that thes…
IIT Mandi（曼迪印度理工学院）；Indraprastha Institute of Information Technology Delhi（德里因德拉普拉斯塔信息技术学院）
In this work, we present a dimensionality reduction algorithm, aka. sketching, for categorical datasets. Our proposed sketching algorithm Cabin constructs low-dimensional binary sketches from high-dimensional categorical vectors, and our distance estimation algorithm Cham computes a close approximation of the Hamming distance between any two original vectors only from their sketches. The minimum dimension of the sketches required by Cham to ensure a good estimation theoretically depends only on the sparsity of the data points - making it useful for many real-life scenarios involving sparse dat…
In this work, we study distributed sketching methods for large scale regression problems. We leverage multiple randomized sketches for reducing the problem dimensions as well as preserving privacy and improving straggler resilience in asynchronous distributed systems. We derive novel approximation guarantees for classical sketching methods and analyze the accuracy of parameter averaging for distributed sketches. We consider random matrices including Gaussian, randomized Hadamard, uniform sampling and leverage score sampling in the distributed setting. Moreover, we propose a hybrid approach com…
Princeton University（普林斯顿大学）；Weizmann Institute of Science（魏茨曼科学研究所）
Recently, there has been much interest in studying the convergence rates of without-replacement SGD, and proving that it is faster than with-replacement SGD in the worst case. However, known lower bounds ignore the problem's geometry, including its condition number, whereas the upper bounds explicitly depend on it. Perhaps surprisingly, we prove that when the condition number is taken into account, without-replacement SGD \emph{does not} significantly improve on with-replacement SGD in terms of worst-case bounds, unless the number of epochs (passes over the data) is larger than the condition n…
