Statistical methods for network data have received a lot of attention because of the wideranging applications of network analysis. There is now a large body of work on methods and models for networks, including the stochastic block model (SBM) [Holland et al., 1983], the degree-corrected stochastic block model (DCSBM) [Karrer and Newman, 2011], and the latent space model [Hoff et al., 2002], to name a few. While this gives the practitioner plenty of choices, there is a lot less work on the crucial question of how to select the best model for the data, as well as how to choose tuning parameters for the selected model, which is often necessary in order to fit it. In some specific problems, progress has been made recently, for instance, in the much-studied problem of community detection. Community detection is the problem of clustering network nodes into groups, and most of the methods proposed over the last twenty years or so require the number of communities K as input.

Today, Financial Institutions (FIs) face significant legal and reputational risks when it comes to complying with anti-money laundering (AML) requirements (including anti-terrorist financing and obligations to conform). Failure can lead to serious sanctions imposed by regulatory bodies (Recently, Societe Generale fined $5.83 MM for a number of shortcomings in its control for preventing money laundering). Today's financial markets are truly global. Transactions and flow of funds take place through a web of interactions across nations and systems. This makes it difficult to be compliant with thousands of regulations and norms across a large number of jurisdictions.

We study the misclassification error for community detection in general heterogeneous stochastic block models (SBM) with noisy or partial label information. We establish a connection between the misclassification rate and the notion of minimum energy on the local neighborhood of the SBM. We develop an optimally weighted message passing algorithm to reconstruct labels for SBM based on the minimum energy flow and the eigenvectors of a certain Markov transition matrix. The general SBM considered in this paper allows for unequal-size communities, degree heterogeneity, and different connection probabilities among blocks. We focus on how to optimally weigh the message passing to improve misclassification.

In this paper we present a comprehensive view of prominent causal discovery algorithms, categorized into two main categories (1) assuming acyclic and no latent variables, and (2) allowing both cycles and latent variables, along with experimental results comparing them from three perspectives: (a) structural accuracy, (b) standard predictive accuracy, and (c) accuracy of counterfactual inference. For (b) and (c) we train causal Bayesian networks with structures as predicted by each causal discovery technique to carry out counterfactual or standard predictive inference. We compare causal algorithms on two pub- licly available and one simulated datasets having different sample sizes: small, medium and large. Experiments show that structural accuracy of a technique does not necessarily correlate with higher accuracy of inferencing tasks. Fur- ther, surveyed structure learning algorithms do not perform well in terms of structural accuracy in case of datasets having large number of variables.

Various measures can be used to estimate bias or unfairness in a predictor. Previous work has already established that some of these measures are incompatible with each other. Here we show that, when groups differ in prevalence of the predicted event, several intuitive, reasonable measures of fairness (probability of positive prediction given occurrence or non-occurrence; probability of occurrence given prediction or non-prediction; and ratio of predictions over occurrences for each group) are all mutually exclusive: if one of them is equal among groups, the other two must differ. The only exceptions are for perfect, or trivial (always-positive or always-negative) predictors. As a consequence, any non-perfect, non-trivial predictor must necessarily be "unfair" under two out of three reasonable sets of criteria. This result readily generalizes to a wide range of well-known statistical quantities (sensitivity, specificity, false positive rate, precision, etc.), all of which can be divided into three mutually exclusive groups. Importantly, The results applies to all predictors, whether algorithmic or human. We conclude with possible ways to handle this effect when assessing and designing prediction methods.

This paper studies the problem of estimating the grahpon model - the underlying generating mechanism of a network. Graphon estimation arises in many applications such as predicting missing links in networks and learning user preferences in recommender systems. The graphon model deals with a random graph of $n$ vertices such that each pair of two vertices $i$ and $j$ are connected independently with probability $\rho \times f(x_i,x_j)$, where $x_i$ is the unknown $d$-dimensional label of vertex $i$, $f$ is an unknown symmetric function, and $\rho$ is a scaling parameter characterizing the graph sparsity. Recent studies have identified the minimax error rate of estimating the graphon from a single realization of the random graph. However, there exists a wide gap between the known error rates of computationally efficient estimation procedures and the minimax optimal error rate. Here we analyze a spectral method, namely universal singular value thresholding (USVT) algorithm, in the relatively sparse regime with the average vertex degree $n\rho=\Omega(\log n)$. When $f$ belongs to H\"{o}lder or Sobolev space with smoothness index $\alpha$, we show the error rate of USVT is at most $(n\rho)^{ -2 \alpha / (2\alpha+d)}$, approaching the minimax optimal error rate $\log (n\rho)/(n\rho)$ for $d=1$ as $\alpha$ increases. Furthermore, when $f$ is analytic, we show the error rate of USVT is at most $\log^d (n\rho)/(n\rho)$. In the special case of stochastic block model with $k$ blocks, the error rate of USVT is at most $k/(n\rho)$, which is larger than the minimax optimal error rate by at most a multiplicative factor $k/\log k$. This coincides with the computational gap observed for community detection. A key step of our analysis is to derive the eigenvalue decaying rate of the edge probability matrix using piecewise polynomial approximations of the graphon function $f$.

An easy way of estimating the test error of a bagged model, without the need for cross-validation is Out-of-Bag Error Estimation. The observations not used to fit a given bagged tree are referred to as the out-of-bag (OOB) observations. We can simply predict the response for the ith observation using each of the trees in which that observation was OOB. We average those predicted responses, or take a majority vote, depending on if the response is quantitative or qualitative. An overall OOB MSE(mean squared error) or classification error rate can be computed.

Over-fitting.If you perform a regression with 200 predictors (with strong cross-correlations among predictors), use meta regression coefficients: that is, use coefficients of the form f[Corr(Var, Response), a,b, c] where a, b, c are three meta-parameters (e.g. This will reduce your number of parameters from 200 to 3, and eliminate most of the over-fitting Perform the right type of cross-validation. If your training set has 400,000 observations distributed across 50 clients, and your test data set (used for cross-validation) has 200,000 observations but only 3 clients or 5 days worth of historical data, then your cross-validation methodology is very flawed. Better, split your cross-validation data set in 5 subsets to compute confidence intervals. Make sure you've eliminated outliers and cleaned your data set.

Cross-validation is a technique used to assess the accuracy of a predictive model, based on training set data. It splits the training sets into test and control sets. The test sets are used to fine-tune the model to increase performance (better classification rate or reduced errors in prediction) and the control sets are used to simulate how the model would perform outside the training set. The control and test sets must be carefully chosen for this method to make sense.

The last decade has seen a surge of interest in adaptive learning algorithms for data stream classification, with applications ranging from predicting ozone level peaks, learning stock market indicators, to detecting computer security violations. In addition, a number of methods have been developed to detect concept drifts in these streams. Consider a scenario where we have a number of classifiers with diverse learning styles and different drift detectors. Intuitively, the current 'best' (classifier, detector) pair is application dependent and may change as a result of the stream evolution. Our research builds on this observation. We introduce the $\mbox{Tornado}$ framework that implements a reservoir of diverse classifiers, together with a variety of drift detection algorithms. In our framework, all (classifier, detector) pairs proceed, in parallel, to construct models against the evolving data streams. At any point in time, we select the pair which currently yields the best performance. We further incorporate two novel stacking-based drift detection methods, namely the $\mbox{FHDDMS}$ and $\mbox{FHDDMS}_{add}$ approaches. The experimental evaluation confirms that the current 'best' (classifier, detector) pair is not only heavily dependent on the characteristics of the stream, but also that this selection evolves as the stream flows. Further, our $\mbox{FHDDMS}$ variants detect concept drifts accurately in a timely fashion while outperforming the state-of-the-art.