"Fraud is a billion-dollar business There are many formal definitions but essentially a fraud is an "art" and crime of deceiving and scamming people in their financial transactions. Frauds have always existed throughout human history but in this age of digital technology, the strategy, extent and magnitude of financial frauds is becoming wide-ranging -- from credit cards transactions to health benefits to insurance claims. Fraudsters are also getting super creative. Who's never received an email from a Nigerian royal widow that she's looking for trusted someone to hand over large sums of her inheritance? No wonder why is fraud a big deal.

Authors suggest their method is a natural generalization of gradient descent to the two-player scenario where the update is given by the Nash equilibrium of a regularized bilinear local approximation of the underlying game. It avoids oscillatory and divergent behaviors seen in alternating gradient descent. The paper proposes several experiments to establish the robustness of their method. This project aims at replicating their results. The paper provides a detailed comparison to methods based on optimism and consensus on the properties of convergence and stability of various discussed methods using numerical experiments and rigorous analysis. In order to understand these terms, comparison and proposed method and examine the results of the experiments, next section gives a necessary background of the original paper. 2 Background The traditional optimization is concerned with a single agent trying to optimize a cost function. It can be seen as min x R m f ( x). The agent has a clear objective to find ("Good local") minimum of f . Gradeint Descent (and its varients) are reliable Algorithmic Baseline for this purpose.

Time series forecasting has gained lots of attention recently; this is because many real-world phenomena can be modeled as time series. The massive volume of data and recent advancements in the processing power of the computers enable researchers to develop more sophisticated machine learning algorithms such as neural networks to forecast the time series data. In this paper, we propose various neural network architectures to forecast the time series data using the dynamic measurements; moreover, we introduce various architectures on how to combine static and dynamic measurements for forecasting. We also investigate the importance of performing techniques such as anomaly detection and clustering on forecasting accuracy. Our results indicate that clustering can improve the overall prediction time as well as improve the forecasting performance of the neural network. Furthermore, we show that feature-based clustering can outperform the distance-based clustering in terms of speed and efficiency. Finally, our results indicate that adding more predictors to forecast the target variable will not necessarily improve the forecasting accuracy.

The agnostic PAC learning model consists of: a Hypothesis Space $\mathcal{H}$, a probability distribution $P$, a sample complexity function $m_{\mathcal{H}}(\epsilon,\delta): [0,1]^{2} \mapsto \mathbb{Z}_{+}$ of precision $\epsilon$ and confidence $1 - \delta$, a finite i.i.d. sample $\mathcal{D}_{N}$, a cost function $\ell$ and a learning algorithm $\mathbb{A}(\mathcal{H},\mathcal{D}_{N})$, which estimates $\hat{h} \in \mathcal{H}$ that approximates a target function $h^{\star} \in \mathcal{H}$ seeking to minimize out-of-sample error. In this model, prior information is represented by $\mathcal{H}$ and $\ell$, while problem solution is performed through their instantiation in several applied learning models, with specific algebraic structures for $\mathcal{H}$ and corresponding learning algorithms. However, these applied models use additional important concepts not covered by the classic PAC learning theory: model selection and regularization. This paper presents an extension of this model which covers these concepts. The main principle added is the selection, based solely on data, of a subspace of $\mathcal{H}$ with a VC-dimension compatible with the available sample. In order to formalize this principle, the concept of Learning Space $\mathbb{L}(\mathcal{H})$, which is a poset of subsets of $\mathcal{H}$ that covers $\mathcal{H}$ and satisfies a property regarding the VC dimension of related subspaces, is presented as the natural search space for model selection algorithms. A remarkable result obtained on this new framework are conditions on $\mathbb{L}(\mathcal{H})$ and $\ell$ that lead to estimated out-of-sample error surfaces, which are true U-curves on $\mathbb{L}(\mathcal{H})$ chains, enabling a more efficient search on $\mathbb{L}(\mathcal{H})$. Hence, in this new framework, the U-curve optimization problem becomes a natural component of model selection algorithms.

The Ideal Observer (IO) performance has been advocated when optimizing medical imaging systems for signal detection tasks. However, analytical computation of the IO test statistic is generally intractable. To approximate the IO test statistic, sampling-based methods that employ Markov-Chain Monte Carlo (MCMC) techniques have been developed. However, current applications of MCMC techniques have been limited to several object models such as a lumpy object model and a binary texture model, and it remains unclear how MCMC methods can be implemented with other more sophisticated object models. Deep learning methods that employ generative adversarial networks (GANs) hold great promise to learn stochastic object models (SOMs) from image data. In this study, we described a method to approximate the IO by applying MCMC techniques to SOMs learned by use of GANs. The proposed method can be employed with arbitrary object models that can be learned by use of GANs, thereby the domain of applicability of MCMC techniques for approximating the IO performance is extended. In this study, both signal-known-exactly (SKE) and signal-known-statistically (SKS) binary signal detection tasks are considered. The IO performance computed by the proposed method is compared to that computed by the conventional MCMC method. The advantages of the proposed method are discussed.

In the context of some machine learning applications, obtaining data instances is a relatively easy process but labeling them could become quite expensive or tedious. Such scenarios lead to datasets with few labeled instances and a larger number of unlabeled ones. Semi-supervised classification techniques combine labeled and unlabeled data during the learning phase in order to increase classifier's generalization capability. Regrettably, most successful semi-supervised classifiers do not allow explaining their outcome, thus behaving like black boxes. However, there is an increasing number of problem domains in which experts demand a clear understanding of the decision process. In this paper, we report on an extended experimental study presenting an interpretable self-labeling grey-box classifier that uses a black box to estimate the missing class labels and a white box to make the final predictions. Two different approaches for amending the self-labeling process are explored: a first one based on the confidence of the black box and the latter one based on measures from Rough Set Theory. The results of the extended experimental study support the interpretability by means of transparency and simplicity of our classifier, while attaining superior prediction rates when compared with state-of-the-art self-labeling classifiers reported in the literature.

Aggregate network properties such as cluster cohesion and the number of bridge nodes can be used to glean insights about a network's community structure, spread of influence and the resilience of the network to faults. Efficiently computing network properties when the network is fully observed has received significant attention (Wasserman and Faust 1994; Cook and Holder 2006), however the problem of computing aggregate network properties when there is missing data attributes has received little attention. Computing these properties for networks with missing attributes involves performing inference over the network. Statistical relational learning (SRL) and graph neural networks (GNNs) are two classes of machine learning approaches well suited for inferring missing attributes in a graph. In this paper, we study the effectiveness of these approaches in estimating aggregate properties on networks with missing attributes. We compare two SRL approaches and three GNNs. For these approaches we estimate these properties using point estimates such as MAP and mean. For SRL-based approaches that can infer a joint distribution over the missing attributes, we also estimate these properties as an expectation over the distribution. To compute the expectation tractably for probabilistic soft logic, one of the SRL approaches that we study, we introduce a novel sampling framework. In the experimental evaluation, using three benchmark datasets, we show that SRL-based approaches tend to outperform GNN-based approaches both in computing aggregate properties and predictive accuracy. Specifically, we show that estimating the aggregate properties as an expectation over the joint distribution outperforms point estimates.

A weakly-supervised learning framework named as complementary-label learning has been proposed recently, where each sample is equipped with a single complementary label that denotes one of the classes the sample does not belong to. However, the existing complementary-label learning methods cannot learn from the easily accessible unlabeled samples and samples with multiple complementary labels, which are more informative. In this paper, to remove these limitations, we propose the novel multi-complementary and unlabeled learning framework that allows unbiased estimation of classification risk from samples with any number of complementary labels and unlabeled samples, for arbitrary loss functions and models. We first give an unbiased estimator of the classification risk from samples with multiple complementary labels, and then further improve the estimator by incorporating unlabeled samples into the risk formulation. The estimation error bounds show that the proposed methods are in the optimal parametric convergence rate. Finally, the experiments on both linear and deep models show the effectiveness of our methods.

In the previous article, we studied the k-NN. One thing that I believe is that if we can correlate anything with us or our lives, there are greater chances of understanding the concept. So I will try to explain everything by relating it to humans. It tries to make the inter-cluster data points as similar as possible while also keeping the clusters as different or as far as possible. It assigns data points to a cluster such that the sum of the squared distance between the data points and the cluster's centroid is at the minimum.

The reproducing Stein kernel approach for post-hoc corrected sampling Liam Hodgkinson 1,, Robert Salomone 2,, and Fred Roosta 3,, † 1 Department of Statistics, UC Berkeley, Berkeley, CA, 94720, USA. Abstract: Stein importance sampling [42] is a widely applicable technique based on kernelized Stein discrepancy [43], which corrects the output of approximate sampling algorithms by reweighting the empirical distribution of the samples. A general analysis of this technique is conducted for the previously unconsidered setting where samples are obtained via the simulation of a Markov chain, and applies to an arbitrary underlying Polish space. We prove that Stein importance sampling yields consistent estimators for quantities related to a target distribution of interest by using samples obtained from a geometrically ergodic Markov chain with a possibly unknown invariant measure that differs from the desired target. The approach is shown to be valid under conditions that are satisfied for a large number of unadjusted samplers, and is capable of retaining consistency when data subsampling is used. Along the way, a universal theory of reproducing Stein kernels is established, which enables the construction of kernelized Stein discrepancy on general Polish spaces, and provides sufficient conditions for kernels to be convergence-determining on such spaces. These results are of independent interest for the development of future methodology based on kernelized Stein discrepancies. 1. Introduction Our problem of interest is the efficient computation of integrals with respect to some target probability measure π . Adopting the Monte Carlo approach, π is approximated by an empirical distribution formed from samples drawn according to π . However, in many problems of interest, it is not possible to simulate according to π exactly, and so further approximate methods must be used. Arguably the most widely employed and general approach is Markov Chain Monte Carlo (MCMC); successively drawing samples as a realization of a Markov chain. The dominant approach to MCMC involves the simulation of a process that is π -ergodic, often constructed by the Metropolis-Hastings algorithm from an underlying irreducible and aperiodic Markov chain [58]. However, there has been significant recent interest in so-called unadjusted MCMC approaches [14, 19, 29, 45]. A common strategy with these methods is the approximate numer-All authors are supported in part by the Australian Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS), under Australian Research Council grant CE140100049. For the same computational effort, one can achieve substantially lower variance of estimates at the cost of incurring additional (asymptotic) bias. Despite poorer asymptotic guarantees [21], the ensuing Markov chains are often rapidly mixing, and perform particularly well in high dimensional settings [20].