213 research outputs found
FastMMD: Ensemble of Circular Discrepancy for Efficient Two-Sample Test
The maximum mean discrepancy (MMD) is a recently proposed test statistic for
two-sample test. Its quadratic time complexity, however, greatly hampers its
availability to large-scale applications. To accelerate the MMD calculation, in
this study we propose an efficient method called FastMMD. The core idea of
FastMMD is to equivalently transform the MMD with shift-invariant kernels into
the amplitude expectation of a linear combination of sinusoid components based
on Bochner's theorem and Fourier transform (Rahimi & Recht, 2007). Taking
advantage of sampling of Fourier transform, FastMMD decreases the time
complexity for MMD calculation from to , where and
are the size and dimension of the sample set, respectively. Here is the
number of basis functions for approximating kernels which determines the
approximation accuracy. For kernels that are spherically invariant, the
computation can be further accelerated to by using the Fastfood
technique (Le et al., 2013). The uniform convergence of our method has also
been theoretically proved in both unbiased and biased estimates. We have
further provided a geometric explanation for our method, namely ensemble of
circular discrepancy, which facilitates us to understand the insight of MMD,
and is hopeful to help arouse more extensive metrics for assessing two-sample
test. Experimental results substantiate that FastMMD is with similar accuracy
as exact MMD, while with faster computation speed and lower variance than the
existing MMD approximation methods
DecideNet: Counting Varying Density Crowds Through Attention Guided Detection and Density Estimation
In real-world crowd counting applications, the crowd densities vary greatly
in spatial and temporal domains. A detection based counting method will
estimate crowds accurately in low density scenes, while its reliability in
congested areas is downgraded. A regression based approach, on the other hand,
captures the general density information in crowded regions. Without knowing
the location of each person, it tends to overestimate the count in low density
areas. Thus, exclusively using either one of them is not sufficient to handle
all kinds of scenes with varying densities. To address this issue, a novel
end-to-end crowd counting framework, named DecideNet (DEteCtIon and Density
Estimation Network) is proposed. It can adaptively decide the appropriate
counting mode for different locations on the image based on its real density
conditions. DecideNet starts with estimating the crowd density by generating
detection and regression based density maps separately. To capture inevitable
variation in densities, it incorporates an attention module, meant to
adaptively assess the reliability of the two types of estimations. The final
crowd counts are obtained with the guidance of the attention module to adopt
suitable estimations from the two kinds of density maps. Experimental results
show that our method achieves state-of-the-art performance on three challenging
crowd counting datasets.Comment: CVPR 201
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