We propose a first data-driven tuning procedure for divide-and-conquer kernel ridge regression (Zhang et al., 2015). While the proposed criterion is computationally scalable for massive data sets, it is also shown to be asymptotically optimal under mild conditions. The effectiveness of our method is illustrated by extensive simulations and an application to Million Song Dataset. Some key words:Distributed GCV, divide-and-conquer, kernel ridge regression, optimal tuning.

Model evaluation metrics are used to assess goodness of fit between model and data, to compare different models, in the context of model selection, and to predict how predictions (associated with a specific model and data set) are expected to be accurate. Confidence intervals are used to assess how reliable a statistical estimate is. Wide confidence intervals mean that your model is poor (and it is worth investigating other models), or that your data is very noisy if confidence intervals don't improve by changing the model (that is, testing a different theoretical statistical distribution for your observations.) Modern confidence intervals are model-free, data -driven: click here to see how to compute them. A more general framework to assess and reduce sources of variance is called analysis of variance.

After you make predictions, you need to know if they are any good. There are standard measures that we can use to summarize how good a set of predictions actually are. Knowing how good a set of predictions is, allows you to make estimates about how good a given machine learning model of your problem, In this tutorial, you will discover how to implement four standard prediction evaluation metrics from scratch in Python. How to implement and interpret a confusion matrix. How to implement mean absolute error for regression.

We demonstrate the possibility of classifying causal systems into kinds that share a common structure without first constructing an explicit dynamical model or using prior knowledge of the system dynamics. The algorithmic ability to determine whether arbitrary systems are governed by causal relations of the same form offers significant practical applications in the development and validation of dynamical models. It is also of theoretical interest as an essential stage in the scientific inference of laws from empirical data. The algorithm presented is based on the dynamical symmetry approach to dynamical kinds. A dynamical symmetry with respect to time is an intervention on one or more variables of a system that commutes with the time evolution of the system. A dynamical kind is a class of systems sharing a set of dynamical symmetries. The algorithm presented classifies deterministic, time-dependent causal systems by directly comparing their exhibited symmetries. Using simulated, noisy data from a variety of nonlinear systems, we show that this algorithm correctly sorts systems into dynamical kinds. It is robust under significant sampling error, is immune to violations of normality in sampling error, and fails gracefully with increasing dynamical similarity. The algorithm we demonstrate is the first to address this aspect of automated scientific discovery.

Polymorphic malware detection is challenging due to the continual mutations miscreants introduce to successive instances of a particular virus. Such changes are akin to mutations in biological sequences. Recently, high-throughput methods for gene sequence classification have been developed by the bioinformatics and computational biology communities. In this paper, we argue that these methods can be usefully applied to malware detection. Unfortunately, gene classification tools are usually optimized for and restricted to an alphabet of four letters (nucleic acids). Consequently, we have selected the Strand gene sequence classifier, which offers a robust classification strategy that can easily accommodate unstructured data with any alphabet including source code or compiled machine code. To demonstrate Stand's suitability for classifying malware, we execute it on approximately 500GB of malware data provided by the Kaggle Microsoft Malware Classification Challenge (BIG 2015) used for predicting 9 classes of polymorphic malware. Experiments show that, with minimal adaptation, the method achieves accuracy levels well above 95% requiring only a fraction of the training times used by the winning team's method.

Analytics is about getting your team the data insights it needs to build better products and make the right decisions for your company. But if your team can't understand that data, then this is all for naught. Software like Amplitude can make your data easy to understand, but each member of your team still needs basic data skills to get the most value out of what they're looking at. These skills can help your team, regardless of whether that's in product or marketing or sales, interpret the data as it comes in. It also gives them the skills to work with your data scientists to propose new ideas for your product, as well as the confidence to work alongside them to improve the business.

Sparsity-based subspace clustering algorithms have attracted significant attention thanks to their excellent performance in practical applications. A prominent example is the sparse subspace clustering (SSC) algorithm by Elhamifar and Vidal, which performs spectral clustering based on an adjacency matrix obtained by sparsely representing each data point in terms of all the other data points via the Lasso. When the number of data points is large or the dimension of the ambient space is high, the computational complexity of SSC quickly becomes prohibitive. Dyer et al. observed that SSC-OMP obtained by replacing the Lasso by the greedy orthogonal matching pursuit (OMP) algorithm results in significantly lower computational complexity, while often yielding comparable performance. The central goal of this paper is an analytical performance characterization of SSC-OMP for noisy data. Moreover, we introduce and analyze the SSC-MP algorithm, which employs matching pursuit (MP) in lieu of OMP. Both SSC-OMP and SSC-MP are proven to succeed even when the subspaces intersect and when the data points are contaminated by severe noise. The clustering conditions we obtain for SSC-OMP and SSC-MP are similar to those for SSC and for the thresholding-based subspace clustering (TSC) algorithm due to Heckel and B\"olcskei. Analytical results in combination with numerical results indicate that both SSC-OMP and SSC-MP with a data-dependent stopping criterion automatically detect the dimensions of the subspaces underlying the data. Moreover, experiments on synthetic and real data show that SSC-MP compares very favorably to SSC, SSC-OMP, TSC, and the nearest subspace neighbor (NSN) algorithm, both in terms of clustering performance and running time. In addition, we find that, in contrast to SSC-OMP, the performance of SSC-MP is very robust with respect to the choice of parameters in the stopping criteria.

Multiple instance learning (MIL) is a form of weakly supervised learning where training instances are arranged in sets, called bags, and a label is provided for the entire bag. This formulation is gaining interest because it naturally fits various problems and allows to leverage weakly labeled data. Consequently, it has been used in diverse application fields such as computer vision and document classification. However, learning from bags raises important challenges that are unique to MIL. This paper provides a comprehensive survey of the characteristics which define and differentiate the types of MIL problems. Until now, these problem characteristics have not been formally identified and described. As a result, the variations in performance of MIL algorithms from one data set to another are difficult to explain. In this paper, MIL problem characteristics are grouped into four broad categories: the composition of the bags, the types of data distribution, the ambiguity of instance labels, and the task to be performed. Methods specialized to address each category are reviewed. Then, the extent to which these characteristics manifest themselves in key MIL application areas are described. Finally, experiments are conducted to compare the performance of 16 state-of-the-art MIL methods on selected problem characteristics. This paper provides insight on how the problem characteristics affect MIL algorithms, recommendations for future benchmarking and promising avenues for research.

New artificial intelligence software designed to spot new child sexual abuse media online could help police catch child abusers. The toolkit, described in a paper published in Digital Investigation, automatically detects new child sexual abuse photos and videos in online peer-to-peer networks. The research behind this technology was conducted in the international research project iCOP - Identifying and Catching Originators in P2P Networks - founded by the European Commission Safer Internet Program by researchers at Lancaster University, the German Research Center for Artificial Intelligence (DFKI), and University College Cork, Ireland. There are hundreds of searches for child abuse images every second worldwide, resulting in hundreds of thousands of child sexual abuse images and videos being shared every year. The people who produce child sexual abuse media are often abusers themselves - the US National Center for Missing and Exploited Children found that 16 percent of the people who possess such media had directly and physically abused children.

The idea of cross-validation is to split the data into N subsets, to put one subset aside, to estimate parameters of the model from the remaining N-1 subsets, and to use the retained subset to estimate the error of the model. Such a process is repeated N times - with each of the N subsets being used as the validation set . Then the values of the errors obtained in such N steps are combined to provide the final estimate of the model error. The cross-validation is used in various classification and prediction procedures, such as regression analysis, discriminant analysis, neural networks and classification and regression trees (CART) . The goal is to improve the quality of the decision that is made from the outcome of the study on the basis of statistical methods, and to ensure that maximum information is obtained from scarce experimental data.