State-of-the-art techniques of artificial intelligence, in particular deep learning, are mostly data-driven. However, collecting and manually labeling a large scale dataset is both difficult and expensive. A promising alternative is to introduce synthesized training data, so that the dataset size can be significantly enlarged with little human labor. But, this raises an important problem in active vision: given an infinite data space, how to effectively sample a finite subset to train a visual classifier? This paper presents an approach for learning from synthesized data effectively. The motivation is straightforward -- increasing the probability of seeing difficult training data. We introduce a module named SampleAhead to formulate the learning process into an online communication between a classifier and a sampler , and update them iteratively. In each round, we adjust the sampling distribution according to the classification results, and train the classifier using the data sampled from the updated distribution. Experiments are performed by introducing synthesized images rendered from ShapeNet models to assist PASCAL3D+ classification. Our approach enjoys higher classification accuracy, especially in the scenario of a limited number of training samples. This demonstrates its efficiency in exploring the infinite data space.
In this paper, we focus on a more efficient sampling strategy. Different from previous work, we consider an infinite (continuous) data space. Instead of sampling from each instance ( e.g. , an image @cite_15 or a regional feature @cite_27 ), we partition the entire data space into a finite number of buckets and perform two-stage sampling, detailed in .
@cite_27 @cite_15
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Random sampling is an appealing approach to build synopses of large data streams because random samples can be used for a broad spectrum of analytical tasks. Users are often interested in analyzing only the most recent fraction of the data stream in order to avoid outdated results. In this paper, we focus on sampling schemes that sample from a sliding window over a recent time interval; such windows are a popular and highly comprehensible method to model recency. In this setting, the main challenge is to guarantee an upper bound on the space consumption of the sample while using the allotted space efficiently at the same time. The difficulty arises from the fact that the number of items in the window is unknown in advance and may vary significantly over time, so that the sampling fraction has to be adjusted dynamically. We consider uniform sampling schemes, which produce each sample of the same size with equal probability, and stratified sampling schemes, in which the window is divided into smaller strata and a uniform sample is maintained per stratum. For uniform sampling, we prove that it is impossible to guarantee a minimum sample size in bounded space. We then introduce a novel sampling scheme called bounded priority sampling (BPS), which requires only bounded space. We derive a lower bound on the expected sample size and show that BPS quickly adapts to changing data rates. For stratified sampling, we propose a merge-based stratification scheme (MBS), which maintains strata of approximately equal size. Compared to naive stratification, MBS has the advantage that the sample is evenly distributed across the window, so that no part of the window is over- or underrepresented. We conclude the paper with a feasibility study of our algorithms on large real-world datasets. Abstract In this paper, we consider the problem of recovering a compactly supported multivariate function from a collection of pointwise samples of its Fourier transform taken nonuniformly. We do this by using the concept of weighted Fourier frames. A seminal result of Beurling shows that sampling points give rise to a classical Fourier frame provided they are relatively separated and of sufficient density. However, this result does not allow for arbitrary clustering of sampling points, as is often the case in practice. Whilst keeping the density condition sharp and dimension independent, our first result removes the separation condition and shows that density alone suffices. However, this result does not lead to estimates for the frame bounds. A known result of Grochenig provides explicit estimates, but only subject to a density condition that deteriorates linearly with dimension. In our second result we improve these bounds by reducing the dimension dependence. In particular, we provide explicit frame bounds which are dimensionless for functions having compact support contained in a sphere. Next, we demonstrate how our two main results give new insight into a reconstruction algorithm—based on the existing generalized sampling framework—that allows for stable and quasi-optimal reconstruction in any particular basis from a finite collection of samples. Finally, we construct sufficiently dense sampling schemes that are often used in practice—jittered, radial and spiral sampling schemes—and provide several examples illustrating the effectiveness of our approach when tested on these schemes. We introduce the problem of sampling from a moving window of recent items from a data stream and develop two algorithms for this problem. The first algorithm, "chain-sample", extends reservoir sampling to deal with the expiration of data elements from the sample. The expected memory usage of our algorithm is O(k) when maintaining a sample of size k over a window of the n most recent elements from the data stream, and with high probability the algorithm requires no more than O(k log n) memory.When the number of elements in the window is variable, as is the case when the size of the window is defined as a time duration rather than as a fixed number of data elements, the sampling problem becomes harder. Our second algorithm, "priority-sample", works even when the number of elements in the window can vary dynamically over time. With high probability, the "priority-sample" algorithm uses no more than O(k log n) memory. In order to efficiently study the characteristics of network domains and support development of network systems (e.g. algorithms, protocols that operate on networks), it is often necessary to sample a representative subgraph from a large complex network. Although recent subgraph sampling methods have been shown to work well, they focus on sampling from memory-resident graphs and assume that the sampling algorithm can access the entire graph in order to decide which nodes edges to select. Many large-scale network datasets, however, are too large and or dynamic to be processed using main memory (e.g., email, tweets, wall posts). In this work, we formulate the problem of sampling from large graph streams. We propose a streaming graph sampling algorithm that dynamically maintains a representative sample in a reservoir based setting. We evaluate the efficacy of our proposed methods empirically using several real-world data sets. Across all datasets, we found that our method produce samples that preserve better the original graph distributions.