Object detection has achieved promising success, but requires large-scale fullyannotated data, which is time-consuming and labor-extensive. Therefore, we consider object detection with mixed supervision, which learns novel object categories using weak annotations with the help of full annotations of existing base object categories. Previous works using mixed supervision mainly learn the classagnostic objectness from fully-annotated categories, which can be transferred to upgrade the weak annotations to pseudo full annotations for novel categories. In this paper, we further transfer mask prior and semantic similarity to bridge the gap between novel categories and base categories. Specifically, the ability of using mask prior to help detect objects is learned from base categories and transferred to novel categories. Moreover, the semantic similarity between objects learned from base categories is transferred to denoise the pseudo full annotations for novel categories. Experimental results on three benchmark datasets demonstrate the effectiveness of our method over existing methods.

We consider the problem of learning mixtures of Gaussians under the constraint of approximate differential privacy. We prove that eO(k2dlog3/2(1/δ)/α2ε) samples are sufficient to learn a mixture of k axis-aligned Gaussians in Rd to within total variation distance αwhile satisfying (ε,δ)-differential privacy. This is the first result for privately learning mixtures of unbounded axis-aligned (or even unbounded univariate) Gaussians. If the covariance matrices of each of the Gaussians is the identity matrix, we show that eO(kd/α2 + kdlog(1/δ)/αε) samples are sufficient. To prove our results, we design a new technique for privately learning mixture distributions. A class of distributions F is said to be list-decodable if there is an algorithm that, given "heavily corrupted" samples from f F, outputs a list of distributions one of which approximates f. We show that if F is privately list-decodable then we can learn mixtures of distributions in F. Finally, we show axis-aligned Gaussian distributions are privately list-decodable, thereby proving mixtures of such distributions are privately learnable.

In recent centralized nonconvex distributed learning and federated learning, local methods are one of the promising approaches to reduce communication time. However, existing work has mainly focused on studying first-order optimality guarantees. On the other side, second-order optimality guaranteed algorithms, i.e., algorithms escaping saddle points, have been extensively studied in the nondistributed optimization literature. In this paper, we study a new local algorithm called Bias-Variance Reduced Local Perturbed SGD (BVR-L-PSGD), that combines the existing bias-variance reduced gradient estimator with parameter perturbation to find second-order optimal points in centralized nonconvex distributed optimization. BVR-L-PSGD enjoys second-order optimality with nearly the same communication complexity as the best known one of BVR-L-SGD to find first-order optimality. Particularly, the communication complexity is better than non-local methods when the local datasets heterogeneity is smaller than the smoothness of the local loss. In an extreme case, the communication complexity approaches to eΘ(1)when the local datasets heterogeneity goes to zero.