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Some commonly used objective loss function such as cross-entropy loss for classification and squared loss for regression can be regarded as special cases of the logarithmic loss function.

"NIPS Neural Information Processing Systems 8-11th December 2014, Montreal, Canada",,, "Paper ID:","1694" "Title:","An Integer Polynomial Programming Based Framework for Lifted MAP Inference" Current Reviews First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The authors propose a new method of performing lifted inference on Markov Logic Networks. The essence of the idea is to encode the MLN as an integer polynomial program, which is then transformed into an integer linear program (which could be solved with a conventional solver such as Gurobi or CPlex). The lifting as preprocessing idea due to Sarkhel et al. is appealing, and this paper extends it using ideas from probabilistic theorem proving. The idea is to extend the list of symmetries recognized by this lifted inference approach (Algorithm 1).

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).

We argue that a good solution should be able to explicitly parameterize a policy (i.e.

Neural Information Processing Systems http://nips.cc/

Your skepticism of growBuf may stem from a shortcoming in our presentation of the method. For most real-world applications, the memory in the chain tends to be fairly local (non-unitary second eigenvalue of the transition matrix), especially in the context of our long chains of interest.

V ariational inference algorithms have proven successful for Bayesian analysis in large data settings, with recent advances using stochastic variational inference (SVI). However, such methods have largely been studied in independent or exchangeable data settings. We develop an SVI algorithm to learn the parameters of hidden Markov models (HMMs) in a time-dependent data setting. The challenge in applying stochastic optimization in this setting arises from dependencies in the chain, which must be broken to consider minibatches of observations. We propose an algorithm that harnesses the memory decay of the chain to adaptively bound errors arising from edge effects. We demonstrate the effectiveness of our algorithm on synthetic experiments and a large genomics dataset where a batch algorithm is computationally infeasible.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This manuscript presents a flexible discrete latent-state model for population neural data. Approximations (variational and eq 10,11) are necessary to do inference in powerful flexible model. This is a tool for confirmatory analysis; one major weakness as a explorative tool is the necessity to set up the state hierarchy in advance. Originality: It is a novel approach.