We present a method for estimating articulated human pose from a single static image based on a graphical model with novel pairwise relations that make adaptive use of local image measurements. More precisely, we specify a graphical model for human pose which exploits the fact the local image measurements can be used both to detect parts (or joints) and also to predict the spatial relationships between them (Image Dependent Pairwise Relations). These spatial relationships are represented by a mixture model. We use Deep Convolutional Neural Networks (DCNNs) to learn conditional probabilities for the presence of parts and their spatial relationships within image patches. Hence our model combines the representational flexibility of graphical models with the efficiency and statistical power of DCNNs. Our method significantly outperforms the state of the art methods on the LSP and FLIC datasets and also performs very well on the Buffy dataset without any training.

The randomized midpoint method, proposed by [ 40 ], has emerged as an optimal discretization procedure for simulating the continuous time underdamped Langevin diffusion. In this paper, we analyze several probabilistic properties of the randomized midpoint discretization method, considering both overdamped and underdamped Langevin dynamics. We first characterize the stationary distribution of the discrete chain obtained with constant step-size discretization and show that it is biased away from the target distribution. Notably, the step-size needs to go to zero to obtain asymptotic unbiasedness. Next, we establish the asymptotic normality of numerical integration using the randomized midpoint method and highlight the relative advantages and disadvantages over other discretizations. Our results collectively provide several insights into the behavior of the randomized midpoint discretization method, including obtaining confidence intervals for numerical integrations.

Equation 9. Therefore if we define a standard "policy" loss L This is the "soft" version of an analogous statement made for "hard" optimality first shown in [32]. This argument is the direct counterpart to Theorem 2 in [32]--which uses argmax instead of softmax. From this point onwards, the same strategy for Proposition 2 again applies, completing the proof. Environments used for experiments are from OpenAI gym [56]. Each environment is associated with a true reward function (unknown to all imitation algorithms).

L-BFGS has been applied as an effective parameter estimation method for various machine learning algorithms since 1980s. With an increasing demand to deal with massive instances and variables, it is important to scale up and parallelize L-BFGS effectively in a distributed system. In this paper, we study the problem of parallelizing the L-BFGS algorithm in large clusters of tens of thousands of shared-nothing commodity machines. First, we show that a naive implementation of L-BFGS using Map-Reduce requires either a significant amount of memory or a large number of map-reduce steps with negative performance impact. Second, we propose a new L-BFGS algorithm, called V ector-free L-BFGS, which avoids the expensive dot product operations in the two loop recursion and greatly improves computation efficiency with a great degree of parallelism. The algorithm scales very well and enables a variety of machine learning algorithms to handle a massive number of variables over large datasets. We prove the mathematical equivalence of the new V ector-free L-BFGS and demonstrate its excellent performance and scalability using real-world machine learning problems with billions of variables in production clusters.

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Recent works leveraging learning to enhance sampling have shown promising results, in particular by designing effective non-local moves and global proposals.

We study the problem of learning a real-valued function that satisfies the Demographic Parity constraint. It demands the distribution of the predicted output to be independent of the sensitive attribute. We consider the case that the sensitive attribute is available for prediction.

We thank all reviewers for their valuable comments. Let us first provide a concise recap of our contributions. We propose an efficient post-processing algorithm (Alg. 1) which can be applied on top of any We highlight that contributions i) and iii) are, up to our knowledge, unique. We now address specific points raised by the reviewers, which will be included in the final version upon acceptance. Let us highlight two key differences between "Wasserstein Fair This is an interesting direction of future research. The main difficulty in such an extension for, e.g., Equalized Odds is due to the conditioning on the Notice also that DP is used in several papers, including Jiang et al. discussed above. Let us disagree that the notion of DP is naive. As stated in the paper (ll. However a form of this assumption is rather classical in non-parametric statistics (see e.g., "Fast learning In our settings As. 4.2 is mostly technical and can be "choice of sigma is left to the user ."

In this paper, we capture the dependence among the labels using a learned tree-structured hierarchy.