We propose a novel training method based on nonlinear multilevel minimization techniques, commonly used for solving discretized large scale partial differential equations. Our multilevel training method constructs a multilevel hierarchy by reducing the number of samples. The training of the original model is then enhanced by internally training surrogate models constructed with fewer samples. We construct the surrogate models using first-order consistency approach. This gives rise to surrogate models, whose gradients are stochastic estimators of the full gradient, but with reduced variance compared to standard stochastic gradient estimators. We illustrate the convergence behavior of the proposed multilevel method to machine learning applications based on logistic regression. A comparison with subsampled Newton's and variance reduction methods demonstrate the efficiency of our multilevel method.

This has made it easier to step outside the rigid model and approximation families designed based on computational tractability, and to switch to flexible distributions parameterized by neural networks, including normalizing flows relying on invertible transformation of simple base distributions [21]. Models with discrete latent variables, however, remain problematic due to non-differentiability of the sampling operation that prevents efficient optimization of expectations over the approximation. Hence in practice, we still largely resort to model-specific algorithms that are tedious to extend already for minor variants of the model, analytic marginalization of the discrete latent variables (e.g., mixture models and LDA in Stan [7]), continuous relaxations like the concrete distribution [19, 13], or (semi-)implicit approximations that do not support probability evaluation [34, 30]. Normalizing flows [25, 15, 21], suitable for learning flexible posterior approximations for continuous variables, have recently been generalized also for discrete categorical [31] and ordinal [12] variables. However, the discrete variants have only been applied in generative modeling of discrete observations. Even though discrete normalizing flows for categorical distributions (DNF) retain the property of differentiable Monte Carlo estimates, they are not very suitable for variational approximation due to their limited expressive power. As we will show later, a DNF can only move probability mass around and hence relies extremely strongly on use of base distributions that are already expressive (and of the same dimension as the final distribution). For generative modeling this can be satisfied, for example by using recurrent neural networks as base distributions in the case of language modeling [31], but for modeling latent variables there are no easy ways of learning strong base distributions. We improve the expressive power of DNFs by constructing mixtures of categorical discrete normalizing flows (MDNF).

In this paper, we propose a confidence-calibration method for predicting the winner of a famous multiplayer online battle arena (MOBA) game, League of Legends. In MOBA games, the dataset may contain a large amount of input-dependent noise; not all of such noise is observable. Hence, it is desirable to attempt a confidence-calibrated prediction. Unfortunately, most existing confidence calibration methods are pertaining to image and document classification tasks where consideration on uncertainty is not crucial. In this paper, we propose a novel calibration method that takes data uncertainty into consideration. The proposed method achieves an outstanding expected calibration error (ECE) (0.57%) mainly owing to data uncertainty consideration, compared to a conventional temperature scaling method of which ECE value is 1.11%.

The display advertising industry has recently transitioned from second- to first-price auctions as its primary mechanism for ad allocation and pricing. In light of this, publishers need to re-evaluate and optimize their auction parameters, notably reserve prices. In this paper, we propose a gradient-based algorithm to adaptively update and optimize reserve prices based on estimates of bidders' responsiveness to experimental shocks in reserves. Our key innovation is to draw on the inherent structure of the revenue objective in order to reduce the variance of gradient estimates and improve convergence rates in both theory and practice. We show that revenue in a first-price auction can be usefully decomposed into a \emph{demand} component and a \emph{bidding} component, and introduce techniques to reduce the variance of each component. We characterize the bias-variance trade-offs of these techniques and validate the performance of our proposed algorithm through experiments on synthetic data and real display ad auctions data from Google ad exchange.

Model usage is the central challenge of model-based reinforcement learning. Although dynamics model based on deep neural networks provide good generalization for single step prediction, such ability is over exploited when it is used to predict long horizon trajectories due to compounding errors. In this work, we propose a Dyna-style model-based reinforcement learning algorithm, which we called Maximum Entropy Model Rollouts (MEMR). To eliminate the compounding errors, we only use our model to generate single-step rollouts. Furthermore, we propose to generate \emph{diverse} model rollouts by non-uniform sampling of the environment states such that the entropy of the model rollouts is maximized. We mathematically derived the maximum entropy sampling criteria for one data case under Gaussian prior. To accomplish this criteria, we propose to utilize a prioritized experience replay. Our preliminary experiments in challenging locomotion benchmarks show that our approach achieves the same sample efficiency of the best model-based algorithms, matches the asymptotic performance of the best model-free algorithms, and significantly reduces the computation requirements of other model-based methods.

Inference problems with conjectured statistical-computational gaps are ubiquitous throughout modern statistics, computer science and statistical physics. While there has been success evidencing these gaps from the failure of restricted classes of algorithms, progress towards a more traditional reduction-based approach to computational complexity in statistical inference has been limited. Existing reductions have largely been limited to inference problems with similar structure -- primarily mapping among problems representable as a sparse submatrix signal plus a noise matrix, which are similar to the common hardness assumption of planted clique. The insight in this work is that a slight generalization of the planted clique conjecture -- secret leakage planted clique -- gives rise to a variety of new average-case reduction techniques, yielding a web of reductions among problems with very different structure. Using variants of the planted clique conjecture for specific forms of secret leakage planted clique, we deduce tight statistical-computational tradeoffs for a diverse range of problems including robust sparse mean estimation, mixtures of sparse linear regressions, robust sparse linear regression, tensor PCA, variants of dense $k$-block stochastic block models, negatively correlated sparse PCA, semirandom planted dense subgraph, detection in hidden partition models and a universality principle for learning sparse mixtures. In particular, a $k$-partite hypergraph variant of the planted clique conjecture is sufficient to establish all of our computational lower bounds. Our techniques also reveal novel connections to combinatorial designs and to random matrix theory. This work gives the first evidence that an expanded set of hardness assumptions, such as for secret leakage planted clique, may be a key first step towards a more complete theory of reductions among statistical problems.

Back in December, when AWS launched its new machine learning IDE, SageMaker Studio, we wrote up a "hot-off-the-presses" review. At the time, we felt the platform fell short, but we promised to publish an update after working with AWS to get more familiar with the new capabilities. When Amazon launched SageMaker Studio, they made clear the pain points they were aiming to solve: "The machine learning development workflow is still very iterative, and is challenging for developers to manage due to the relative immaturity of ML tooling." The machine learning workflow -- from data ingestion, feature engineering, and model selection to debugging, deployment, monitoring, and maintenance, along with all the steps in between -- can be like trying to tame a wild animal. To solve this challenge, big tech companies have built their own machine learning and big data platforms for their data scientists to use: Uber has Michelangelo, Facebook (and likely Instagram and WhatsApp) has FBLearner flow, Google has TFX, and Netflix has both Metaflow and Polynote (the latter has been open sourced).

Then this course is for you! This course has been designed by two professional Data Scientists so that we can share our knowledge and help you learn complex theory, algorithms, and coding libraries in a simple way. We will walk you step-by-step into the World of Machine Learning. With every tutorial, you will develop new skills and improve your understanding of this challenging yet lucrative sub-field of Data Science. This course is fun and exciting, but at the same time, we dive deep into Machine Learning.

Principal Component Analysis is used to reduce the number of dimensions (features) in a dataset. Say, we have 10 dimensions/features in our dataset. It's not a smart way to just drop 7–8 features based on an assumption (or a wild guess). One method to tackle this problem could be a feature selection technique (say, Chi-Squared). Feature Selection Techniques help us select the most important'k' features corresponding to the target feature.

Can I become a data scientist with little or no math background? What essential math skills are important in data science? There are so many good packages that can be used for building predictive models or for producing data visualizations. Thanks to these packages, anyone can build a model or produce a data visualization. However, very solid background knowledge in mathematics is essential for fine-tuning your models to produce reliable models with optimal performance.