Statistical Learning
On Education Python for Data Science and Machine Learning Bootcamp - CouponED
Use Python for Data Science and Machine Learning Use Spark for Big Data Analysis Implement Machine Learning Algorithms Learn to use NumPy for Numerical Data Learn to use Pandas for Data Analysis Learn to use Matplotlib for Python Plotting Learn to use Seaborn for statistical plots Use Plotly for interactive dynamic visualizations Use SciKit-Learn for Machine Learning Tasks Random Forest and Decision Trees Natural Language Processing and Spam Filters Support Vector Machines Some programming experience Admin permissions to download files Are you ready to start your path to becoming a Data Scientist! This comprehensive course will be your guide to learning how to use the power of Python to analyze data, create beautiful visualizations, and use powerful machine learning algorithms! Data Scientist has been ranked the number one job on Glassdoor and the average salary of a data scientist is over $120,000 in the United States according to Indeed! Data Science is a rewarding career that allows you to solve some of the world's most interesting problems! This course is designed for both beginners with some programming experience or experienced developers looking to make the jump to Data Science!
How It Feels to Learn Data Science in 2019
So I just have to buy a Tableau license and I'm now a data scientist? Okay, let's just take that sales pitch with a grain of salt. I may be clueless, but I know there is more to data science than making pretty visualizations. I can do that in Excel. You got to admit it is slick marketing though. Charting data is the fun stage, and they leave out the painful and time-consuming parts of working with data: cleaning, wrangling, transforming, and loading it. Yes, and that is why I suspect there is value in learning to code. Maybe you can learn Alteryx. There's another software called Alteryx that allows you to clean, wrangle, transform, and load data.
Deep Value Model Predictive Control
Farshidian, Farbod, Hoeller, David, Hutter, Marco
In this paper, we introduce an actor-critic algorithm called Deep Value Model Predictive Control (DMPC), which combines model-based trajectory optimization with value function estimation. The DMPC actor is a Model Predictive Control (MPC) optimizer with an objective function defined in terms of a value function estimated by the critic. We show that our MPC actor is an importance sampler, which minimizes an upper bound of the cross-entropy to the state distribution of the optimal sampling policy. In our experiments with a Ballbot system, we show that our algorithm can work with sparse and binary reward signals to efficiently solve obstacle avoidance and target reaching tasks. Compared to previous work, we show that including the value function in the running cost of the trajectory optimizer speeds up the convergence. We also discuss the necessary strategies to robustify the algorithm in practice.
Learning event representations in image sequences by dynamic graph embedding
Dimiccoli, Mariella, Wendt, Herwig
Recently, self-supervised learning has proved to be effective to learn representations of events in image sequences, where events are understood as sets of temporally adjacent images that are semantically perceived as a whole. However, although this approach does not require expensive manual annotations, it is data hungry and suffers from domain adaptation problems. As an alternative, in this work, we propose a novel approach for learning event representations named Dynamic Graph Embedding (DGE). The assumption underlying our model is that a sequence of images can be represented by a graph that encodes both semantic and temporal similarity. The key novelty of DGE is to learn jointly the graph and its graph embedding. At its core, DGE works by iterating over two steps: 1) updating the graph representing the semantic and temporal structure of the data based on the current data representation, and 2) updating the data representation to take into account the current data graph structure. The main advantage of DGE over state-of-the-art self-supervised approaches is that it does not require any training set, but instead learns iteratively from the data itself a low-dimensional embedding that reflects their temporal and semantic structure. Experimental results on two benchmark datasets of real image sequences captured at regular intervals demonstrate that the proposed DGE leads to effective event representations. In particular, it achieves robust temporal segmentation on the EDUBSeg and EDUBSeg-Desc benchmark datasets, outperforming the state of the art.
Algorithmic Probability-guided Supervised Machine Learning on Non-differentiable Spaces
Hernández-Orozco, Santiago, Zenil, Hector, Riedel, Jürgen, Uccello, Adam, Kiani, Narsis A., Tegnér, Jesper
We show how complexity theory can be introduced in machine learning to help bring together apparently disparate areas of current research. We show that this new approach requires less training data and is more generalizable as it shows greater resilience to random attacks. We investigate the shape of the discrete algorithmic space when performing regression or classification using a loss function parametrized by algorithmic complexity, demonstrating that the property of differentiation is not necessary to achieve results similar to those obtained using differentiable programming approaches such as deep learning. In doing so we use examples which enable the two approaches to be compared (small, given the computational power required for estimations of algorithmic complexity). We find and report that (i) machine learning can successfully be performed on a non-smooth surface using algorithmic complexity; (ii) that parameter solutions can be found using an algorithmic-probability classifier, establishing a bridge between a fundamentally discrete theory of computability and a fundamentally continuous mathematical theory of optimization methods; (iii) a formulation of an algorithmically directed search technique in non-smooth manifolds can be defined and conducted; (iv) exploitation techniques and numerical methods for algorithmic search to navigate these discrete non-differentiable spaces can be performed; in application of the (a) identification of generative rules from data observations; (b) solutions to image classification problems more resilient against pixel attacks compared to neural networks; (c) identification of equation parameters from a small data-set in the presence of noise in continuous ODE system problem, (d) classification of Boolean NK networks by (1) network topology, (2) underlying Boolean function, and (3) number of incoming edges.
A Test for Shared Patterns in Cross-modal Brain Activation Analysis
Kalinina, Elena, Pedregosa, Fabian, Iacovella, Vittorio, Olivetti, Emanuele, Avesani, Paolo
Determining the extent to which different cognitive modalities (understood here as the set of cognitive processes underlying the elaboration of a stimulus by the brain) rely on overlapping neural representations is a fundamental issue in cognitive neuroscience. In the last decade, the identification of shared activity patterns has been mostly framed as a supervised learning problem. For instance, a classifier is trained to discriminate categories (e.g. faces vs. houses) in modality I (e.g. perception) and tested on the same categories in modality II (e.g. imagery). This type of analysis is often referred to as cross-modal decoding. In this paper we take a different approach and instead formulate the problem of assessing shared patterns across modalities within the framework of statistical hypothesis testing. We propose both an appropriate test statistic and a scheme based on permutation testing to compute the significance of this test while making only minimal distributional assumption. We denote this test cross-modal permutation test (CMPT). We also provide empirical evidence on synthetic datasets that our approach has greater statistical power than the cross-modal decoding method while maintaining low Type I errors (rejecting a true null hypothesis). We compare both approaches on an fMRI dataset with three different cognitive modalities (perception, imagery, visual search). Finally, we show how CMPT can be combined with Searchlight analysis to explore spatial distribution of shared activity patterns.
Learning Near-optimal Convex Combinations of Basis Models with Generalization Guarantees
Nguyen, Tan, Ye, Nan, Bartlett, Peter L.
The problem of learning an optimal convex combination of basis models has been studied in a number of works, with a focus on the theoretical analysis, but little investigati on on the empirical performance of the approach. In this paper, we present some new theoretical insights, and empirical resul ts that demonstrate the effectiveness of the approach. Theore ti-cally, we first consider whether we can replace convex combinations by linear combinations, and obtain convergence r e-sults similar to existing results for learning from a convex hull. We present a negative result showing that the linear hull of very simple basis functions can have unbounded capacity, an d is thus prone to overfitting. On the other hand, convex hulls are still rich but have bounded capacities. In addition, we o b-tain a generalization bound for a general class of Lipschitz loss functions. Empirically, we first discuss how a convex combination can be greedily learned with early stopping, an d how a convex combination can be non-greedily learned when the number of basis models is known a priori. Our experiments suggest that the greedy scheme is competitive with or better than several baselines, including boosting and rand om forests. The greedy algorithm requires little effort in hyp er-parameter tuning, and also seems to adapt to the underlying complexity of the problem.
Penalized regression via the restricted bridge estimator
Yüzbaşı, Bahadır, Arashi, Mohammad, Akdeniz, Fikri
This article is concerned with the Bridge Regression, which is a special family in penalized regression with penalty function $\sum_{j=1}^{p}|\beta_j|^q$ with $q>0$, in a linear model with linear restrictions. The proposed restricted bridge (RBRIDGE) estimator simultaneously estimates parameters and selects important variables when a prior information about parameters are available in either low dimensional or high dimensional case. Using local quadratic approximation, the penalty term can be approximated around a local initial values vector and the RBRIDGE estimator enjoys a closed-form expression which can be solved when $q>0$. Special cases of our proposal are the restricted LASSO ($q=1$), restricted RIDGE ($q=2$), and restricted Elastic Net ($1< q < 2$) estimators. We provide some theoretical properties of the RBRIDGE estimator under for the low dimensional case, whereas the computational aspects are given for both low and high dimensional cases. An extensive Monte Carlo simulation study is conducted based on different prior pieces of information and the performance of the RBRIDGE estiamtor is compared with some competitive penalty estimators as well as the ORACLE. We also consider four real data examples analysis for comparison sake. The numerical results show that the suggested RBRIDGE estimator outperforms outstandingly when the prior is true or near exact
Stochastic Triangular Mesh Mapping
Lombard, Clint D., van Daalen, Corné E.
For mobile robots to operate autonomously in general environments, perception is required in the form of a dense metric map. For this purpose, we present the stochastic triangular mesh (STM) mapping technique: a 2.5-D representation of the surface of the environment using a continuous mesh of triangular surface elements, where each surface element models the mean plane and roughness of the underlying surface. In contrast to existing mapping techniques, a STM map models the structure of the environment by ensuring a continuous model, while also being able to be incrementally updated with linear computational cost in the number of measurements. We reduce the effect of uncertainty in the robot pose (position and orientation) by using landmark-relative submaps. The uncertainty in the measurements and robot pose are accounted for by the use of Bayesian inference techniques during the map update. We demonstrate that a STM map can be used with sensors that generate point measurements, such as light detection and ranging (LiDAR) sensors and stereo cameras. We show that a STM map is a more accurate model than the only comparable online surface mapping technique$\unicode{x2014}$a standard elevation map$\unicode{x2014}$and we also provide qualitative results on practical datasets.
Variance reduction for Markov chains with application to MCMC
Belomestny, D., Iosipoi, L., Moulines, E., Naumov, A., Samsonov, S.
D. Belomestny, L. Iosipoi † E. Moulines ‡, A. Naumov §, and S. Samsonov ¶ Abstract In this paper we propose a novel variance reduction approach for additive functionals of Markov chains based on minimization of an estimate for the asymptotic variance of these functionals over suitable classes of control variates. A distinctive feature of the proposed approach is its ability to significantly reduce the overall finite sample variance. This feature is theoretically demonstrated by means of a deep non asymptotic analysis of a variance reduced functional as well as by a thorough simulation study. In particular we apply our method to various MCMC Bayesian estimation problems where it favourably compares to the existing variance reduction approaches. 1 Introduction Variance reduction methods play nowadays a prominent role as a complexity reduction tool in simulation based numerical algorithms like Monte Carlo (MC) or Markov Chain Monte Carlo (MCMC).