"Differentiable Convex Optimization Layers"

CVXPY creates powerful new PyTorch and TensorFlow layers

Agrawal et al.: https://locuslab.github.io/2019-10-28-cvxpylayers/

#PyTorch #TensorFlow #NeurIPS2019


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Streamlit, a Python framework that dedicates to deploying Machine Learning and Data Science models. If you are a data scientist who's struggling to showcase your fantastic works, I would encourage you to check it out.

The author had a nice article/ tutorial at Med:

#machinelearning #mlops
#datascience

Github link:
https://github.com/streamlit/streamlit

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Don't confuse creating a data product and deployment. Streamlit makes creating a GUI-type data product easy for Python, much like shiny makes it easy for R.

Deployment is the next step: running it on a server, having security and user authentication, scaling it as required, updating the application when necessary, etc.

That's what the ownR platform does for shiny and dash already and will soon offer for Streamlit too. If you need to actually deploy your data products, especially in an enterprise environment, drop me an invite or a DM for a demo or a trial account!

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What Are "Panel Models?"​ Part 1

In #statistics, the English is sometimes as hard as the math. Vocabulary is frequently used in confusing ways and often differs by discipline. "Panel" and "longitudinal" are two examples - economists tend to favor the first term, while researchers in most other fields use the second to mean essentially the same thing.

But to what "thing" do they refer? Say, for example, households, individual household members, companies or brands are selected and followed over time. Statisticians working in many fields, such as economics and psychology, have developed numerous techniques which allow us to study how these households, household members, companies or brands change over time, and investigate what might have caused these changes.

Marketing mix modeling conducted at the category level is one example that will be close to home for many marketing researchers. In a typical case, we might have four years of weekly sales and marketing data for 6-8 brands in a product or service category. These brands would comprise the panel. This type of modeling is also known as cross-sectional time-series analysis because there is an explicit time component in the modeling. It is just one kind of panel/longitudinal analysis.

Marketing researchers make extensive use of online panels for consumer surveys. Panelists are usually not surveyed on the same topic on different occasions though they can be, in which case we would have a panel selected from an online panel. Some MROCs (aka insights communities) also are large and can be analyzed with these methods.

The reference manual for the Stata statistical software provides an in-depth look at many of these methods, particularly those widely-used in econometrics. I should note that there is a methodological connection with mixed-effects models, which I have briefly summarized here. Mplus is another statistical package which is popular among researchers in psychology, education and healthcare, and its website is another good resource.
Longitudinal/panel modeling has featured in countless papers and conference presentations over the years and is also the subject of many books. Here are some books I have found helpful:

Analysis of Longitudinal Data (Diggle et al.)
Analysis of Panel Data (Hsiao)
Econometric Analysis of Panel Data (Baltagi)
Longitudinal Structural Equation Modeling (Newsom)
Growth Modeling (Grimm et al.)
Longitudinal Analysis (Hoffman)
**Applied Longitudinal Data Analysis for Epidemiology (Twisk)**

Many of these methods can also be performed within a Bayesian statistical framework.

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What Are "Panel Models?" Part 2

Rather than having been displaced by big data, AI and machine learning, these techniques are more valuable than ever because we now have more longitudinal data than ever. Many longitudinal methods are computationally intensive and not suitable for massive data on ordinary computers, but parallel processing and cloud computing will often get around this. I also anticipate that more big data versions of their computational algorithms will be developed over the next few years. Here is one example.

For those new to the subject who would like a quick (if somewhat technical) start, I’ve included some edited entries from the Stata reference manual’s glossary below.

Any copy/paste and editing errors are mine.

Arellano–Bond estimator. The Arellano–Bond estimator is a generalized method of moments (GMM) estimator for linear dynamic panel-data models that uses lagged levels of the endogenous variables as well as first differences of the exogenous variables as instruments. The Arellano–Bond estimator removes the panel-specific heterogeneity by first-differencing the regression equation.

autoregressive process. In autoregressive processes, the current value of a variable is a linear function of its own past values and a white-noise error term.

balanced data. A longitudinal or panel dataset is said to be balanced if each panel has the same number of observations.

between estimator. The between estimator is a panel-data estimator that obtains its estimates by running OLS on the panel-level means of the variables. This estimator uses only the between-panel variation in the data to identify the parameters, ignoring any within-panel variation. For it to be consistent, the between estimator requires that the panel-level means of the regressors be uncorrelated with the panel-specific heterogeneity terms.

correlation structure. A correlation structure is a set of assumptions imposed on the within-panel variance–covariance matrix of the errors in a panel-data model.

cross-sectional data. Cross-sectional data refers to data collected over a set of individuals, such as households, firms, or countries sampled from a population at a given point in time.

cross-sectional time-series data. Cross-sectional time-series data is another name for panel data. The term cross-sectional time-series data is sometimes reserved for datasets in which a relatively small number of panels were observed over many periods. See also panel data.

disturbance term. The disturbance term encompasses any shocks that occur to the dependent variable that cannot be explained by the conditional (or deterministic) portion of the model.

dynamic model. A dynamic model is one in which prior values of the dependent variable or disturbance term affect the current value of the dependent variable.

endogenous variable. An endogenous variable is a regressor that is correlated with the unobservable error term. Equivalently, an endogenous variable is one whose values are determined by the equilibrium or outcome of a structural model.

exogenous variable. An exogenous variable is a regressor that is not correlated with any of the unobservable error terms in the model. Equivalently, an exogenous variable is one whose values change independently of the other variables in a structural model.

fixed-effects model. The fixed-effects model is a model for panel data in which the panel-specific errors are treated as fixed parameters. These parameters are panel-specific intercepts and therefore allow the conditional mean of the dependent variable to vary across panels. The linear fixed effects estimator is consistent, even if the regressors are correlated with the fixed effects.

generalized estimating equations (GEE). The method of generalized estimating equations is used to fit population-averaged panel-data models. GEE extends the GLM method by allowing the user to specify a variety of different within-panel correlation structures.

generalized linear model. The generalized linear model is an estimation framework in which the user specifies a distributional family for the dependent variable and a link function that relates the dependent variable to a linear combination of the regressors. The distribution must be a member of the exponential family of distributions. The generalized linear model encompasses many common models, including linear, probit, and Poisson regression.

idiosyncratic error term. In longitudinal or panel-data models, the idiosyncratic error term refers to the observation-specific zero-mean random-error term. It is analogous to the random-error term of cross-sectional regression analysis.

instrumental variables. Instrumental variables are exogenous variables that are correlated with one or more of the endogenous variables in a structural model. The term instrumental variable is often reserved for those exogenous variables that are not included as regressors in the model.

instrumental-variables (IV) estimator. An instrumental variables estimator uses instrumental variables to produce consistent parameter estimates in models that contain endogenous variables. IV estimators can also be used to control for measurement error.

longitudinal data. Longitudinal data is another term for panel data.

overidentifying restrictions. The order condition for model identification requires that the number of exogenous variables excluded from the model be at least as great as the number of endogenous regressors. When the number of excluded exogenous variables exceeds the number of endogenous regressors, the model is overidentified, and the validity of the instruments can then be checked via a test of overidentifying restrictions.

panel data. Panel data are data in which the same units were observed over multiple periods. The units, called panels, are often firms, households, or patients who were observed at several points in time. In a typical panel dataset, the number of panels is large, and the number of observations per panel is relatively small.

panel-corrected standard errors (PCSEs). The term panel-corrected standard errors refers to a class of estimators for the variance–covariance matrix of the OLS estimator when there are relatively few panels with many observations per panel. PCSEs account for heteroskedasticity, autocorrelation, or cross-sectional correlation.

pooled estimator. A pooled estimator ignores the longitudinal or panel aspect of a dataset and treats the observations as if they were cross-sectional.

population-averaged model. A population-averaged model is used for panel data in which the parameters measure the effects of the regressors on the outcome for the average individual in the population. The panel-specific errors are treated as uncorrelated random variables drawn from a population with zero mean and constant variance, and the parameters measure the effects of the regressors on the dependent variable after integrating over the distribution of the random effects.

predetermined variable. A predetermined variable is a regressor in which its contemporaneous and future values are not correlated with the unobservable error term but past values are correlated with the error term.

prewhiten. To prewhiten is to apply a transformation to a time series so that it becomes white noise.

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What Are "Panel Models?" Part 3​

random-coefficients model. A random-coefficients model is a panel-data model in which group specific heterogeneity is introduced by assuming that each group has its own parameter vector, which is drawn from a population common to all panels.

random-effects model. A random-effects model for panel data treats the panel-specific errors as uncorrelated random variables drawn from a population with zero mean and constant variance. The regressors must be uncorrelated with the random effects for the estimates to be consistent.

regressand. The regressand is the variable that is being explained or predicted in a regression model. Synonyms include dependent variable, left-hand-side variable, and endogenous variable.

regressor. Regressors are variables in a regression model used to predict the regressand. Synonyms include independent variable, right-hand-side variable, explanatory variable, predictor variable, and exogenous variable.

strongly balanced. A longitudinal or panel dataset is said to be strongly balanced if each panel has the same number of observations and the observations for different panels were all made at the same times.

unbalanced data. A longitudinal or panel dataset is said to be unbalanced if each panel does not have the same number of observations.

weakly balanced. A longitudinal or panel dataset is said to be weakly balanced if each panel has the same number of observations but the observations for different panels were not all made at the same times.

within estimator. The within estimator is a panel-data estimator that removes the panel-specific heterogeneity by subtracting the panel-level means from each variable and then performing ordinary least squares on the demeaned data. The within estimator is used in fitting the linear fixed-effects model.

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What is Cluster Analysis?

Practically anyone working in marketing research or data science has heard of cluster analysis, but there are many misunderstandings about what it is. This is not surprising since cluster analysis originated outside the business world and is frequently applied in ways we may not be familiar with.

#Clusteranalysis is actually not just one thing and is an umbrella term for a very large family of methods which includes familiar approaches such as K-means and hierarchical agglomerative clustering (HAC). For those of you interested in a detailed look at cluster analysis, below are some excellent if technical books on or related to cluster analysis:

Cluster Analysis (Everitt et al.)
* Data Clustering (Aggarwal and Reddy)
* Handbook of Cluster Analysis (Hennig et al.)
* Applied Biclustering Methods (Kasim et al.)
* Finite Mixture and Markov Switching Models (Frühwirth-Schnatter)
* Latent Class and Latent Transition Analysis (Collins and Lanza)
* Advances in Latent Class Analysis (Hancock et al.)
* Market Segmentation (Wedel and Kamakura)

"Cluster analysis – also known as unsupervised learning – is used in multivariate statistics to uncover latent groups suspected in the data or to discover groups of homogeneous observations. The aim is thus often defined as partitioning the data such that the groups are as dissimilar as possible and that the observations within the same group are as similar as possible. The groups forming the partition are also referred to as clusters.

Cluster analysis can be used for different purposes. It can be employed
(1) as an exploratory tool to detect structure in multivariate data sets such that the results allow the data to be summarized and represented in a simplified and shortened form,
(2) to perform vector quantization and compress the data using suitable prototypes and prototype assignments and
(3) to reveal a latent group structure which corresponds to unobserved heterogeneity.
A standard statistical textbook on cluster analysis is, for example, Everitt et al. (2011).

Clustering is often referred to as an ill-posed problem which aims to reveal interesting structures in the data or to derive a useful grouping of the observations. However, specifying what is interesting or useful in a formal way is challenging. This complicates the specification of suitable criteria for selecting a clustering method or a final clustering solution. Hennig (2015) also emphasizes this point. He argues that the definition of the true clusters depends on the context and on the aim of clustering. Thus there does not exist a unique clustering solution given the data, but different aims of clustering imply different solutions, and analysts should in general be aware of the ambiguity inherent in cluster analysis and thus be transparent about their clustering aims when presenting the solutions obtained.

At the core of cluster analysis is the definition of what a cluster is. This can be achieved by defining the characteristics of the clusters which should emerge as output from the analysis. Often these characteristics can only be informally defined and are not directly useful for selecting a suitable clustering method. In addition, some notion of the total number of clusters suspected or the expected size of clusters might be needed to characterize the cluster problem. Furthermore, domain knowledge is important for deciding on a suitable solution, in the sense that the derived partition consists of interpretable clusters that have practical relevance. However, domain experts are often only able to assess the suitability of a solution once they are confronted with a grouping but are unable to provide clear characteristics of the desired clustering beforehand."

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What are the three types of error in a #ML model?

👉 1. Bias - error caused by choosing an algorithm that cannot accurately model the signal in the data, i.e. the model is too general or was incorrectly selected. For example, selecting a simple linear regression to model highly non-linear data would result in error due to bias.

👉 2. Variance - error from an estimator being too specific and learning relationships that are specific to the training set but do not generalize to new samples well. Variance can come from fitting too closely to noise in the data, and models with high variance are extremely sensitive to changing inputs. Example: Creating a decision tree that splits the training set until every leaf node only contains 1 sample.

👉 3. Irreducible error - error caused by noise in the data that cannot be removed through modeling. Example: inaccuracy in data collection causes irreducible error.

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Kick-start your Python Career with 56 amazing Python Open source Projects
#python #programming #technology #project

https://data-flair.training/blogs/python-open-source-projects/

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Wherefore Multivariate Regression?

Multivariate analysis (MVA), in a regression setting, typically implies that a single dependent variable (outcome) is modeled as a function of two or more independent variables (predictors).

There are situations, though, in which we have two or more dependent variables we wish to model simultaneously, multivariate regression being one example. I tend to approach this through a structural equation modeling (SEM) framework but there are several alternatives.

Why not run one #regression for each outcome? There are several reasons, and the excerpt below from Multilevel Analysis: An Introduction to Basic and Advanced Multilevel Modeling (Snijders and Bosker) is a particularly succinct explanation in the context of multilevel models.

"Why analyze multiple dependent variables simultaneously? It is possible to analyze all m dependent variables separately. There are several reasons why it may be sensible to analyze the data jointly, that is, as multivariate data.

1. Conclusions can be drawn about the correlations between the dependent variables – notably, the extent to which the unexplained correlations depend on the individual and on the group level. Such conclusions follow from the partitioning of the covariances between the dependent variables over the levels of analysis.

2. The tests of specific effects for single dependent variables are more powerful in the multivariate analysis. This will be visible in the form of smaller standard errors. The additional power is negligible if the dependent variables are only weakly correlated, but may be considerable if the dependent variables are strongly correlated while at the same time the data are very incomplete, that is, the average number of measurements available per individual is considerably less than m.

3. Testing whether the effect of an explanatory variable on dependent variable Y1 is larger than its effect on Y2, when the data on Y1 and Y2 were observed (totally or partially) on the same individuals, is possible only by means of a multivariate analysis.

4. If one wishes to carry out a single test of the joint effect of an explanatory variable on several dependent variables, then a multivariate analysis is also required. Such a single test can be useful, for example, to avoid the danger of capitalization on chance which is inherent in carrying out a separate test for each dependent variable.

A multivariate analysis is more complicated than separate analyses for each dependent variable. Therefore, when one wishes to analyze several dependent variables, the greater complexity of the multivariate analysis will have to be balanced against the reasons listed above. Often it is advisable to start by analyzing the data for each dependent variable separately."

Source: Multilevel Analysis: An Introduction to Basic and Advanced Multilevel Modeling, Tom Snijders

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Data Science Life Cycle


#artificialintellegence #machinelearning

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Introduction to Autoencoders - Unsupervised Deep Learning Models (Cont'd) | Coursera

https://bit.ly/2Nw5CCh

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Can We Learn the Language of Proteins?

#DataScience #MachineLearning #ArtificialIntelligence

http://bit.ly/33jCof6

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