Previous work on predicting or generating 3D human pose sequences regresses either joint rotations or joint positions. The former strategy is prone to error accumulation along the kinematic chain, as well as discontinuities when using Euler angles or exponential maps as parameterizations. The latter requires re-projection onto skeleton constraints to avoid bone stretching and invalid configurations. This work addresses both limitations. QuaterNet represents rotations with quaternions and our loss function performs forward kinematics on a skeleton to penalize absolute position errors instead of angle errors. We investigate both recurrent and convolutional architectures and evaluate on short-term prediction and long-term generation. For the latter, our approach is qualitatively judged as realistic as recent neural strategies from the graphics literature. Our experiments compare quaternions to Euler angles as well as exponential maps and show that only a very short context is required to make reliable future predictions. Finally, we show that the standard evaluation protocol for Human3.6M produces high variance results and we propose a simple solution.

In this paper we propose a novel neural language modelling (NLM) method based on \textit{error-correcting output codes} (ECOC), abbreviated as ECOC-NLM. This latent variable based approach provides a principled way to choose a varying amount of latent output codes and avoids exact softmax normalization. Instead of minimizing measures between the predicted probability distribution and true distribution, we use error-correcting codes to represent both predictions and outputs. Secondly, we propose multiple ways to improve accuracy and convergence rates by maximizing the separability between codes that correspond to classes proportional to word embedding similarities. Lastly, we introduce a novel method called \textit{Latent Mixture Sampling}, a technique that is used to mitigate exposure bias and can be integrated into training latent-based neural language models. This involves mixing the latent codes (i.e variables) of past predictions and past targets in one of two ways: (1) according to a predefined sampling schedule or (2) a differentiable sampling procedure whereby the mixing probability is learned throughout training by replacing the greedy argmax operation with a smooth approximation. In evaluating Codeword Mixture Sampling for ECOC-NLM, we also baseline it against CWMS in a closely related Hierarhical Softmax-based NLM.

Abstract--In this letter, we introduce a distributed Nesterov method, termed as ABN, that does not require doubly-stochastic weight matrices. Instead, the implementation is based on a simultaneous application of both row-and column-stochastic weights that makes this method applicable to arbitrary (stronglyconnected) graphs.Since constructing column-stochastic weights needs additional information (the number of outgoing neighbors at each agent), not available in certain communication protocols, we derive a variation, termed as FROZEN, that only requires row-stochastic weights but at the expense of additional iterations for eigenvector learning. We numerically study these algorithms for various objective functions and network parameters and show that the proposed distributed Nesterov methods achieve acceleration compared to the current state-of-the-art methods for distributed optimization. I. INTRODUCTION Distributed optimization has recently seen a surge of interest particularly with the emergence of modern signal processing and machine learning applications. A well-studied problem in this domain is finite sum minimization that also has some relevance to empirical risk formulations, i.e., min R is a smooth and convex function available at an agent i. 's depend on data that may be private to each agent and communicating large data is impractical, developing distributed solutions of the above problem have attracted a strong interest.

Label shift refers to the phenomenon where the marginal probability p(y) of observing a particular class changes between the training and test distributions while the conditional probability p(x|y) stays fixed. This is relevant in settings such as medical diagnosis, where a classifier trained to predict disease based on observed symptoms may need to be adapted to a different distribution where the baseline frequency of the disease is higher. Given calibrated estimates of p(y|x), one can apply an EM algorithm to correct for the shift in class imbalance between the training and test distributions without ever needing to calculate p(x|y). Unfortunately, modern neural networks typically fail to produce well-calibrated probabilities, compromising the effectiveness of this approach. Although Temperature Scaling can greatly reduce miscalibration in these networks, it can leave behind a systematic bias in the probabilities that still poses a problem. To address this, we extend Temperature Scaling with class-specific bias parameters, which largely eliminates systematic bias in the calibrated probabilities and allows for effective domain adaptation under label shift. We term our calibration approach "Bias-Corrected Temperature Scaling". On experiments with CIFAR10, we find that EM with Bias-Corrected Temperature Scaling significantly outperforms both EM with Temperature Scaling and the recently-proposed Black-Box Shift Estimation.

Loss functions with a large number of saddle points are one of the main obstacles to training many modern machine learning models. Gradient descent (GD) is a fundamental algorithm for machine learning and converges to a saddle point for certain initial data. We call the region formed by these initial values the "attraction region." For quadratic functions, GD converges to a saddle point if the initial data is in a subspace of up to n-1 dimensions. In this paper, we prove that a small modification of the recently proposed Laplacian smoothing gradient descent (LSGD) [Osher, et al., arXiv:1806.06317] contributes to avoiding saddle points without sacrificing the convergence rate of GD. In particular, we show that the dimension of the LSGD's attraction region is at most floor((n-1)/2) for a class of quadratic functions which is significantly smaller than GD's (n-1)-dimensional attraction region.

We present a novel cross-view classification algorithm where the gallery and probe data come from different views. A popular approach to tackle this problem is the multi-view subspace learning (MvSL) that aims to learn a latent subspace shared by multi-view data. Despite promising results obtained on some applications, the performance of existing methods deteriorates dramatically when the multi-view data is sampled from nonlinear manifolds or suffers from heavy outliers. To circumvent this drawback, motivated by the Divide-and-Conquer strategy, we propose Multi-view Hybrid Embedding (MvHE), a unique method of dividing the problem of cross-view classification into three subproblems and building one model for each subproblem. Specifically, the first model is designed to remove view discrepancy, whereas the second and third models attempt to discover the intrinsic nonlinear structure and to increase discriminability in intra-view and inter-view samples respectively. The kernel extension is conducted to further boost the representation power of MvHE. Extensive experiments are conducted on four benchmark datasets. Our methods demonstrate overwhelming advantages against the state-of-the-art MvSL based cross-view classification approaches in terms of classification accuracy and robustness.

Which authors of this paper are endorsers? Disable MathJax (What is MathJax?)

It is a gradient descent algorithm for classification implemented from scratch using numpy library. It is good practice to shuffle data at first numpy.random.shuffle() Mini Batch Size is size of input data flowing through network at a time for calculating error as a whole Learning Rate Alpha decides the rate at which, weights and biases will update while back propagation Number of Epochs decides number of times, the whole dataset will be used to train the network Set Mini Batch Size to 1/10th of total data available. And update it manually after every train of network to find its optimum value Alpha should be selected such that learning isn't very slow as well as it didn't take long jump or else, network will start diverging from local minima Number of epochs are selected such that network don't overfit itself over noise In ANN, output will depend on every neuron it pass through For output layer, we have label according to which, it is possible to find it's expected value But for all other layers, there is no single solution available So, finding optimum value is little harder for that

We're here to discuss analysis of data, learning of skills and implementation of web analytics.

In this article, you will discover XGBoost and get a gentle introduction to what it is, where it came from and how you can learn more. Bagging: It is an approach where you take random samples of data, build learning algorithms and take simple means to find bagging probabilities. Boosting: Boosting is similar, however, the selection of sample is made more intelligently. We subsequently give more and more weight to hard to classify observations. XGBoost is an optimized distributed gradient boosting library designed to be highly efficient, flexible and portable.