In this work, we show for the first time that error compensated gradient compression methods can be accelerated. In particular, we propose and study the error compensated loopless Katyusha method, and establish an accelerated linear convergence rate under standard assumptions.

If the labels are given from a discrete set, the trees are usually called classification trees, and otherwise they are usually called regression trees .

The latter allows us to control the error in the stochastic gradient updates due to inaccurate solution to both subproblems.

We implement several representative supervised classification algorithms in ADBench (as shown in Appx. B.1), and recommend interesting readers to recent machine learning books [ To this end, some recent studies investigate efficiently using partially labeled data for improving detection performance, and leverage the unlabeled data to facilitate representation learning. As we show in Table 1, there is a line of existing AD benchmarks. A GAN-based method that defines the reconstruction error of the input instance as the anomaly score. The hidden size of REPEN is set to 20, and the margin of triplet loss is set to 1000.

Figure 1 provides an overview of ADBench.

The above lemma is obtained by combining [ CGM19, Corollary 7] and VC-dimension bounds. We now prove the accuracy guarantee of Algorithm 1 . Here, we give the details of Algorithm 4 invoked in step 4 of Algorithm 2 . Note that the setup in Algorithm 2 is a special case of the above. Moreover, Algorithm 2 requires O ( m log ( m) log ( 1)) gradient computations.

We present a series of new differentially private (DP) algorithms with dimension-independent margin guarantees.