Imbalanced response variable distribution is not an uncommon occurrence in data science. One common way to combat class imbalance is through resampling the minority class to achieve a more balanced distribution. In this paper, we investigate the performance of the sampling method based on kernel density estimate (KDE). We illustrate how KDE is less prone to overfitting than other standard sampling methods. Numerical experiments show that KDE can outperform other sampling techniques on a range of classifiers and real life datasets.

A fundamental problem arising in many areas of machine learning is the evaluation of the likelihood of a given observation under different nominal distributions. Frequently, these nominal distributions are themselves estimated from data, which makes them susceptible to estimation errors. We thus propose to replace each nominal distribution with an ambiguity set containing all distributions in its vicinity and to evaluate an \emph{optimistic likelihood}, that is, the maximum of the likelihood over all distributions in the ambiguity set. When the proximity of distributions is quantified by the Fisher-Rao distance or the Kullback-Leibler divergence, the emerging optimistic likelihoods can be computed efficiently using either geodesic or standard convex optimization techniques. We showcase the advantages of working with optimistic likelihoods on a classification problem using synthetic as well as empirical data.

Clustering high-dimensional data, such as images or biological measurements, is a long-standing problem and has been studied extensively. Recently, Deep Clustering gained popularity due to the non-linearity of neural networks, which allows for flexibility in fitting the specific peculiarities of complex data. Here we introduce the Mixture-of-Experts Similarity Variational Autoencoder (MoE-Sim-VAE), a novel generative clustering model. The model can learn multi-modal distributions of high-dimensional data and use these to generate realistic data with high efficacy and efficiency. MoE-Sim-VAE is based on a Variational Autoencoder (VAE), where the decoder consists of a Mixture-of-Experts (MoE) architecture. This specific architecture allows for various modes of the data to be automatically learned by means of the experts. Additionally, we encourage the latent representation of our model to follow a Gaussian mixture distribution and to accurately represent the similarities between the data points. We assess the performance of our model on synthetic data, the MNIST benchmark data set, and a challenging real-world task of defining cell subpopulations from mass cytometry (CyTOF) measurements on hundreds of different datasets. MoE-Sim-VAE exhibits superior clustering performance on all these tasks in comparison to the baselines and we show that the MoE architecture in the decoder reduces the computational cost of sampling specific data modes with high fidelity.

Energy-Based Models (EBMs) outputs unmormalized log-probability values given data samples. Such an estimation is essential in a variety of applications such as sample generation, denoising, sample restoration, outlier detection, Bayesian reasoning, and many more. However, standard maximum likelihood training is computationally expensive due to the requirement of sampling the model distribution. Score matching potentially alleviates this problem, and denoising score matching is a particularly convenient version. However, previous works do not produce models capable of high quality sample synthesis in high dimensional datasets from random initialization. We believe that is because the score is only matched over a single noise scale, which corresponds to a small set in high-dimensional space. To overcome this limitation, here we instead learn an energy function using denoising score matching over all noise scales. When sampled from random initialization using Annealed Langevin Dynamics and single-step denoising jump, our model produced high-quality samples comparable to state-of-the-art techniques such as GANs. The learned model also provide density information and set a new sample quality baseline in energy-based models. We further demonstrate that the proposed method generalizes well with an image inpainting task.

This scenario is dir ectly analogous to longitudinal causal inference problems with multiple time-varying treatments that conta in time-varying confounders, variables that serve as confounders for some treatments and as mediators for othe r treatments. If there is an unmeasured con-founder for the R -Y relationship (represented by V and the dashed arrows in Figure 1 (a)), then conditioning on R fails to identify the direct effects of A on Y, because it opens a confounding pathway through V . See Hernan and Robins (2020) for an overview of these issues. The answer to the question posed in Appendix B of WB, "Can the c auses be causally dependent among themselves?" is therefore "no." If they are causally depend ent then the deconfounder, by dint of rendering the causes independent, breaks some of the structure among t he causes A, and as was originally established in the time-varying treatment setting, this undermines the identification of joint effects of A on Y by covariate adjustment. Analysis of Lemma 4. This simple argument also serves as a counterexample to Lemm a 4, which states that the deconfounder does not pick up any post-treatment va riables and can be treated as a pre-treatment covariate. This is necessarily false whenever the causes ar e causally dependent among themselves, but it need not hold even if the causes are not causally dependent, s ee below. The proof of Lemma 4 in Appendix I states that "Inferring the s ubstitute confounder Z

Within the context of empirical risk minimization, see Raginsky, Rakhlin, and Telgarsky (2017), we are concerned with a non-asymptotic analysis of sampling algorithms used in optimization. In particular, we obtain non-asymptotic error bounds for a popular class of algorithms called Stochastic Gradient Langevin Dynamics (SGLD). These results are derived in appropriate Wasserstein distances in the absence of the log-concavity of the target distribution. More precisely, the local Lipschitzness of the stochastic gradient $H(\theta, x)$ is assumed, and furthermore, the dissipativity and convexity at infinity condition are relaxed by removing the uniform dependence in $x$.

Information spreads on complex social networks extremely fast, in other words, a piece of information can go viral within no time. Often it is hard to barricade this diffusion prior to the significant occurrence of chaos, be it a social media or an online coding platform. GitHub is one such trending online focal point for any business to reach their potential contributors and customers, simultaneously. By exploiting such software development paradigm, millions of free software emerged lately in diverse communities. To understand human influence, information spread and evolution of transmitted information among assorted users in GitHub, we developed a deep neural network model: "DeepFork", a supervised machine learning based approach that aims to predict information diffusion in complex social networks; considering node as well as topological features. In our empirical studies, we observed that information diffusion can be detected by link prediction using supervised learning. DeepFork outperforms other machine learning models as it better learns the discriminative patterns from the input features. DeepFork aids in understanding information spread and evolution through a bipartite network of users and repositories i.e., information flow from a user to repository to user.

If you've heard of quantum computing, you might be excited about the possibility of applying it to machine learning applications. I work at Springboard, and we recently launched a machine learning bootcamp that includes a job guarantee. We want to make sure our graduates are exposed to cutting-edge machine learning applications -- so we put together this article as part of our research into the intersection of quantum computing and machine learning. Let's start by examining the difference between quantum computing and classical computing. In classical computing, your data is stored in physical bits and it is binary and mutually exhaustive: a bit is either in a 0 state or in a 1 state and it cannot be both at the same time.

Enter the following standard SQL query in the Query editor text area. When the query is complete, click the Results tab below the query text area. The results tab shows the columns you queried that are used to train your model: station_name, duration, num_trips, distance_from_city_center. The results should look like the following. Now that you have examined your training data, the next step is to create a k-means model using the data. You can create and train a k-means model using the CREATE MODEL statement with the option model_type kmeans.

After modeling, the next stage is always analyzing how our model is performing and why it is doing what it's doing. However, if you've had the chance to work with ensemble methods, you probably already know that these algorithms are usually known as "black-box models". These models lack explicability and interpretability since the way they usually work implies one or several layers of a machine making decisions without human supervision, apart from a group of rules or parameters set. More often than not, not even the most expert professionals in the field can understand the function that is actually created by, for example, training a neural network. In this sense, some of the most classical machine learning models were actually better. That's why, for the sake of this post, we'll be analyzing the feature importance of our project using a classic Logistic Regression.