Technical quality I am currently on the fence with respect to technical quality, but hope the authors can clarify the following in the rebuttal. The starting point for the method is a divergence D_f(P Q) which we aim to minimize. Unfortunately, the mini-max objective function of Eq. (6) is a lower-bound on this divergence. This seems problematic as optimizing Eq (6) would then not guarantee anything with respect to the original divergence, regardless of how tight the bound is. This is in stark contrast to variational EM, which maximizes a lower-bound on the log-likelihood, a quantity we also aim to maximize.

In deep learning, classification tasks are formalized as optimization problems solved via the minimization of the cross-entropy. However, recent advancements in the design of objective functions allow the $f$-divergence measure to generalize the formulation of the optimization problem for classification. With this goal in mind, we adopt a Bayesian perspective and formulate the classification task as a maximum a posteriori probability problem. We propose a class of objective functions based on the variational representation of the $f$-divergence, from which we extract a list of five posterior probability estimators leveraging well-known $f$-divergences. In addition, driven by the challenge of improving the state-of-the-art approach, we propose a bottom-up method that leads us to the formulation of a new objective function (and posterior probability estimator) corresponding to a novel $f$-divergence referred to as shifted log (SL). First, we theoretically prove the convergence property of the posterior probability estimators. Then, we numerically test the set of proposed objective functions in three application scenarios: toy examples, image data sets, and signal detection/decoding problems. The analyzed tasks demonstrate the effectiveness of the proposed estimators and that the SL divergence achieves the highest classification accuracy in almost all the scenarios.

In the first part of this Blog series on Kaggle Competition for G2Net Gravitational Wave Detection I discussed the introduction on Gravitational waves, fundamentals of digital signal processing. In this part-2, I will be doing simple EDA on this dataset and building a baseline ConvNet Model with Keras. In this competition, you are provided with a training set of time series data containing simulated gravitational wave measurements from a network of 3 gravitational wave interferometers (LIGO Hanford, LIGO Livingston, and Virgo). Each time series contains either detector noise or detector noise plus a simulated gravitational wave signal. The task is to identify when a signal is present in the data (target 1).

Before we see how the tf.data API works, let's review how we usually train a Keras model. First, we need a dataset. An example is the fashion MNIST dataset that comes with the Keras API, which we have 60,000 training samples and 10,000 test samples of 28 28 pixels in grayscale and the corresponding classification label is encoded with integers 0 to 9. The dataset is a NumPy array. Then we can build a Keras model for classification, and with the model's fit() function, we provide the NumPy array as data.

Python is an awesome programming language! It is one of the most popular languages for developing AI and machine learning applications. With a very easy to learn syntax, Python has some special features that distinguish it from other languages. Python Special Features Photo by M Mani, some rights reserved. The libraries used in this tutorial are imported in the code below.

All of a sudden, your program becomes asynchronous – it can do useful things while it waits for other things, such as I/O operations, to complete. Code written in the async/await style looks like regular synchronous code but works very differently. To understand how it works, one should be familiar with many non-trivial concepts including concurrency, parallelism, event loops, I/O multiplexing, asynchrony, cooperative multitasking and coroutines. Python's implementation of async/await adds even more concepts to this list: generators, generator-based coroutines, native coroutines, yield and yield from. Because of this complexity, many Python programmers that use async/await do not realize how it actually works. I believe that it should not be the case. The async/await pattern can be explained in a simple manner if you start from the ground up. And that's what we're going to do today. Note: In this post I'm referring to CPython 3.9. Some implementation details will certainly change as CPython evolves. I'll try to keep track of important changes and add update notes. Computers execute programs sequentially – one instruction after another. But a typical program performs multiple tasks, and it doesn't always make sense to wait for some task to complete before starting the next one. For example, a chess program that waits for a player to make a move should be able to update the clock in the meantime. Such an ability of a program to deal with multiple things simultaneously is what we call concurrency. Concurrency doesn't mean that multiple tasks must run at the same physical time.

We propose a new generative modeling technique for learning multidimensional cumulative distribution functions (CDFs) in the form of copulas. Specifically, we consider certain classes of copulas known as Archimedean and hierarchical Archimedean copulas, popular for their parsimonious representation and ability to model different tail dependencies. We consider their representation as mixture models with Laplace transforms of latent random variables from generative neural networks. This alternative representation allows for computational efficiencies and easy sampling, especially in high dimensions. We describe multiple methods for optimizing the network parameters. Finally, we present empirical results that demonstrate the efficacy of our proposed method in learning multidimensional CDFs and its computational efficiency compared to existing methods.

The parameters are usually fitted only on the basis of experimental results. The squashing function (also soft cutting or soft clipping function) introduced above stands out of the other candidates by having a theoretical background thanks to the nilpotent logic which lies behind the scenes. In, 17 Klimek and Perelstein presented a Neural Network (NN) algorithm optimized to perform a Monte Carlo methods, which are widely used in particle physics to integrate and sample probability distributions on multidimensional phase spaces. The algorithm has been applied to several examples of direct relevance for particle physics, including situations with nontrivial features such as sharp resonances and soft/collinear enhancements. In this algorithm, each node in a hidden layer of the NN takes a linear combination of the outputs of the nodes in the previous layer and applies an activation function.