Computing part scores is the main computational bottleneck in object detection with Deformable Part Models. In this work we introduce an efficient method to obtain bounds on part scores, which we then integrate with deformable model detection. As in [1] we rapidly approximate the inner product between a weight vector and HOG-based features by quantizing the HOG cells onto a codebook and replace...

In analysis of Boolean functions, a halfspace is a function f : {−1, 1}n → {0, 1} of the form f(x) = 1{a · x > t}, where ∑ i a i = 1. We show that if f is a halfspace with E[f ] = ǫ, then the degree-1 Fourier weight of f is W (f) = Θ(ǫ log(1/ǫ)), and the maximal influence of f is Imax(f) = Θ(ǫmin(1, a ′ √ log(1/ǫ))), where a = maxi |ai|. These results, which determine the exact asymptotic order...

We consider a stochastic N -particle model for the spatially homogeneous Boltzmann evolution and show its convergence to the associated Boltzmann equation when N −→ ∞. More precisely, for any time T > 0 we bound over the distance between the empirical measure of the particle system and the measure given by Boltzmann evolution. That distance is computed in some homogeneous Sobolev space. The con...

In this short note we will present two stability properties of the Chernoff-Ou-Pan inequality, newly obtained in [6], which states that if K is a convex domain in the plane R2 with area a(K) , then one gets a(K) 1 k ∫ π k 0 ωk(θ )wk ( θ + π k ) dθ , where wk(θ ) is defined in [6] (see also §3 below), and the equality holds if and only if K is a circular disc. Mathematics subject classification ...

Quantum theory imposes a strict limit on the strength of non-local correlations. It only allows for a violation of the CHSH inequality up to the value 2 √ 2, known as Tsirelson’s bound. In this note, we consider generalized CHSH inequalities based on many measurement settings with two possible measurement outcomes each. We demonstrate how to prove Tsirelson bounds for any such generalized CHSH ...

To determine the sharp constants for the one dimensional Lieb– Thirring inequalities with exponent γ ∈ (1/2, 3/2) is still an open problem. According to a conjecture by Lieb and Thirring the sharp constant for these exponents should be attained by potentials having only one bound state. Here we exhibit a connection between the Lieb–Thirring conjecture for γ = 1 and an isporimetric inequality fo...

Meshalkin’s theorem states that a class of ordered p-partitions of an n-set has at most max ( n a1,...,ap ) members if for each k the k parts form an antichain. We give a new proof of this and the corresponding LYM inequality due to Hochberg and Hirsch, which is simpler and more general than previous proofs. It extends to a common generalization of Meshalkin’s theorem and Erdős’s theorem about ...

We derive exponential tail inequalities for sums of random matrices with no dependence on the explicit matrix dimensions. These are similar to the matrix versions of the Chernoff bound and Bernstein inequality except with the explicit matrix dimensions replaced by a trace quantity that can be small even when the dimension is large or infinite. Some applications to principal component analysis a...

Here I share a few notes I used in various course lectures, talks, etc. Some may be just calculations that in the textbooks are more complicated, scattered, or less specific; others may be simple observations I found useful or curious. 1 Nemirovski Estimate of Mean of Arbitrary Distributions with Bounded Variance The popular Chernoff bounds assume severe restrictions on distribution: it must be...

We present a new class of service for location based social networks, called the Flexible Group Spatial Keyword ‹ery, which enables a group of users to collectively €nd a point of interest (POI) that optimizes an aggregate cost function combining both spatial distances and keyword similarities. In addition, our query service allows users to consider the trade-o‚s between obtaining a suboptimal ...