To ensure the security of the general mass, crime prevention is one of the most higher priorities for any government. An accurate crime prediction model can help the government, law enforcement to prevent violence, detect the criminals in advance, allocate the government resources, and recognize problems causing crimes. To construct any future-oriented tools, examine and understand the crime patterns in the earliest possible time is essential. In this paper, I analyzed a real-world crime and accident dataset of Denver county, USA, from January 2014 to May 2019, which containing 478,578 incidents. This project aims to predict and highlights the trends of occurrence that will, in return, support the law enforcement agencies and government to discover the preventive measures from the prediction rates. At first, I apply several statistical analysis supported by several data visualization approaches. Then, I implement various classification algorithms such as Random Forest, Decision Tree, AdaBoost Classifier, Extra Tree Classifier, Linear Discriminant Analysis, K-Neighbors Classifiers, and 4 Ensemble Models to classify 15 different classes of crimes. The outcomes are captured using two popular test methods: train-test split, and k-fold cross-validation. Moreover, to evaluate the performance flawlessly, I also utilize precision, recall, F1-score, Mean Squared Error (MSE), ROC curve, and paired-T-test. Except for the AdaBoost classifier, most of the algorithms exhibit satisfactory accuracy. Random Forest, Decision Tree, Ensemble Model 1, 3, and 4 even produce me more than 90% accuracy. Among all the approaches, Ensemble Model 4 presented superior results for every evaluation basis. This study could be useful to raise the awareness of peoples regarding the occurrence locations and to assist security agencies to predict future outbreaks of violence in a specific area within a particular time.

A variety of lifted inference algorithms, which exploit model symmetry to reduce computational cost, have been proposed to render inference tractable in probabilistic relational models. Most existing lifted inference algorithms operate only over discrete domains or continuous domains with restricted potential functions, e.g., Gaussian. We investigate two approximate lifted variational approaches that are applicable to hybrid domains and expressive enough to capture multi-modality. We demonstrate that the proposed variational methods are both scalable and can take advantage of approximate model symmetries, even in the presence of a large amount of continuous evidence. We demonstrate that our approach compares favorably against existing message-passing based approaches in a variety of settings. Finally, we present a sufficient condition for the Bethe approximation to yield a non-trivial estimate over the marginal polytope.

For many years, achievements and discoveries made by scientists are made aware through research papers published in appropriate journals or conferences. Often, established scientists and especially newbies are caught up in the dilemma of choosing an appropriate conference to get their work through. Every scientific conference and journal is inclined towards a particular field of research and there is a vast multitude of them for any particular field. Choosing an appropriate venue is vital as it helps in reaching out to the right audience and also to further one's chance of getting their paper published. In this work, we address the problem of recommending appropriate conferences to the authors to increase their chances of acceptance. We present three different approaches for the same involving the use of social network of the authors and the content of the paper in the settings of dimensionality reduction and topic modeling. In all these approaches, we apply Correspondence Analysis (CA) to derive appropriate relationships between the entities in question, such as conferences and papers. Our models show promising results when compared with existing methods such as content-based filtering, collaborative filtering and hybrid filtering.

Spectral clustering is a very important and classic graph clustering method. Its clustering results are heavily dependent on affine matrix produced by data. Solving Low-Rank Representation~(LRR) problems is a very effective method to obtain affine matrix. This paper proposes LRR factorization model based on group norm regularization and uses Augmented Lagrangian Method~(ALM) algorithm to solve this model. We adopt group norm regularization to make the columns of the factor matrix sparse, thereby achieving the purpose of low rank. And no Singular Value Decomposition~(SVD) is required, computational complexity of each step is great reduced. We get the affine matrix by different LRR model and then perform cluster testing on synthetic noise data and real data~(Hopkin155 and EYaleB) respectively. Compared to traditional models and algorithms, ours are faster to solve affine matrix and more robust to noise. The final clustering results are better. And surprisingly, the numerical results show that our algorithm converges very fast, and the convergence condition is satisfied in only about ten steps. Group norm regularized LRR factorization model with the algorithm designed for it is effective and fast to obtain a better affine matrix.

Current prognostic risk scores in cardiac surgery are based on statistics and do not yet benefit from machine learning. Statistical predictors are not robust enough to correctly identify patients who would benefit from Transcatheter Aortic Valve Implantation (TAVI). This research aims to create a machine learning model to predict one-year mortality of a patient after TAVI. We adopt a modern gradient boosting on decision trees algorithm, specifically designed for categorical features. In combination with a recent technique for model interpretations, we developed a feature analysis and selection stage, enabling to identify the most important features for the prediction. We base our prediction model on the most relevant features, after interpreting and discussing the feature analysis results with clinical experts. We validated our model on 270 TAVI cases, reaching an AUC of 0.83. Our approach outperforms several widespread prognostic risk scores, such as logistic EuroSCORE II, the STS risk score and the TAVI2-score, which are broadly adopted by cardiologists worldwide.

In high dimension, low sample size (HDLSS) settings, the simple average distance classifier based on the Euclidean distance performs poorly if differences between the locations get masked by the scale differences. To rectify this issue, modifications to the average distance classifier was proposed by Chan and Hall (2009). However, the existing classifiers cannot discriminate when the populations differ in other aspects than locations and scales. In this article, we propose some simple transformations of the average distance classifier to tackle this issue. The resulting classifiers perform quite well even when the underlying populations have the same location and scale. The high-dimensional behavior of the proposed classifiers is studied theoretically. Numerical experiments with a variety of simulated as well as real data sets exhibit the usefulness of the proposed methodology. 1 INTRODUCTION Let us consider a classification problem involving two unknown multivariate distribution functions F 1 and F 2 on R D .

In unconstrained optimisation on an Euclidean space, to prove convergence in Gradient Descent processes (GD) $x_{n+1}=x_n-\delta _n \nabla f(x_n)$ it usually is required that the learning rates $\delta _n$'s are bounded: $\delta _n\leq \delta $ for some positive $\delta $. Under this assumption, if the sequence $x_n$ converges to a critical point $z$, then with large values of $n$ the update will be small because $||x_{n+1}-x_n||\lesssim ||\nabla f(x_n)||$. This may also force the sequence to converge to a bad minimum. If we can allow, at least theoretically, that the learning rates $\delta _n$'s are not bounded, then we may have better convergence to better minima. A previous joint paper by the author showed convergence for the usual version of Backtracking GD under very general assumptions on the cost function $f$. In this paper, we allow the learning rates $\delta _n$ to be unbounded, in the sense that there is a function $h:(0,\infty)\rightarrow (0,\infty )$ such that $\lim _{t\rightarrow 0}th(t)=0$ and $\delta _n\lesssim \max \{h(x_n),\delta \}$ satisfies Armijo's condition for all $n$, and prove convergence under the same assumptions as in the mentioned paper. It will be shown that this growth rate of $h$ is best possible if one wants convergence of the sequence $\{x_n\}$. A specific way for choosing $\delta _n$ in a discrete way connects to Two-way Backtracking GD defined in the mentioned paper. We provide some results which either improve or are implicitly contained in those in the mentioned paper and another recent paper on avoidance of saddle points.

This paper proposes a semi-sequential probabilistic model (SSP) that applies an additional short term memory to enhance the performance of the probabilistic indoor localization. The conventional probabilistic methods normally treat the locations in the database indiscriminately. In contrast, SSP leverages the information of the previous position to determine the probable location since the user's speed in an indoor environment is bounded and locations near the previous one have higher probability than the other locations. Although the SSP utilizes the previous location information, it does not require the exact moving speed and direction of the user. On-site experiments using the received signal strength indicator (RSSI) and channel state information (CSI) fingerprints for localization demonstrate that SSP reduces the maximum error and boosts the performance of existing probabilistic approaches by 25% - 30%.

XGBoost was originally developed by Tianqi Chen in his paper titeled "XGBoost: A Scalable Tree Boosting System." XGBoost itself is an enhancement to the gradient boosting algorithm created by Jerome H. Friedman in his paper titled "Greedy Function Approximation: A Gradient Boosting Machine." Both papers are well worth exploring.

We formally prove the connection between k-means clustering and the predictions of neural networks based on the softmax activation layer. In existing work, this connection has been analyzed empirically, but it has never before been mathematically derived. The softmax function partitions the transformed input space into cones, each of which encompasses a class. This is equivalent to putting a number of centroids in this transformed space at equal distance from the origin, and k-means clustering the data points by proximity to these centroids. Softmax only cares in which cone a data point falls, and not how far from the centroid it is within that cone. We formally prove that networks with a small Lipschitz modulus (which corresponds to a low susceptibility to adversarial attacks) map data points closer to the cluster centroids, which results in a mapping to a k-means-friendly space. To leverage this knowledge, we propose Centroid Based Tailoring as an alternative to the softmax function in the last layer of a neural network. The resulting Gauss network has similar predictive accuracy as traditional networks, but is less susceptible to one-pixel attacks; while the main contribution of this paper is theoretical in nature, the Gauss network contributes empirical auxiliary benefits.