Expectation-maximization for logistic regression

We present a family of expectation-maximization (EM) algorithms for binary and negative-binomial logistic regression, drawing a sharp connection with the variational-Bayes algorithm of Jaakkola and Jordan (2000). Indeed, our results allow a version of this variational-Bayes approach to be re-interpreted as a true EM algorithm. We study several interesting features of the algorithm, and of this previously unrecognized connection with variational Bayes. We also generalize the approach to sparsity-promoting priors, and to an online method whose convergence properties are easily established. This latter method compares favorably with stochastic-gradient descent in situations with marked collinearity

Complex Event Recognition from Images with Few Training Examples

We propose to leverage concept-level representations for complex event recognition in photographs given limited training examples. We introduce a novel framework to discover event concept attributes from the web and use that to extract semantic features from images and classify them into social event categories with few training examples. Discovered concepts include a variety of objects, scenes, actions and event sub-types, leading to a discriminative and compact representation for event images. Web images are obtained for each discovered event concept and we use (pretrained) CNN features to train concept classifiers. Extensive experiments on challenging event datasets demonstrate that our proposed method outperforms several baselines using deep CNN features directly in classifying images into events with limited training examples. We also demonstrate that our method achieves the best overall accuracy on a dataset with unseen event categories using a single training example.Comment: Accepted to Winter Applications of Computer Vision (WACV'17

Universal features of Lifshitz Green's functions from holography

We examine the behavior of the retarded Green's function in theories with Lifshitz scaling symmetry, both through dual gravitational models and a direct field theory approach. In contrast with the case of a relativistic CFT, where the Green's function is fixed (up to normalization) by symmetry, the generic Lifshitz Green's function can a priori depend on an arbitrary function $\mathcal G(\hat\omega)$, where $\hat\omega=\omega/|\vec k|^z$ is the scale-invariant ratio of frequency to wavenumber, with dynamical exponent $z$. Nevertheless, we demonstrate that the imaginary part of the retarded Green's function (i.e. the spectral function) of scalar operators is exponentially suppressed in a window of frequencies near zero. This behavior is universal in all Lifshitz theories without additional constraining symmetries. On the gravity side, this result is robust against higher derivative corrections, while on the field theory side we present two $z=2$ examples where the exponential suppression arises from summing the perturbative expansion to infinite order.Comment: 32 pages, 4 figures, v2: reference added, v3: fixed bug in bibliograph