A central subject in Condensed Matter Physics and Statistical Mechanics is the study of phase transitions and critical phenomena [1, 2]. In the last decades, due to the increasing computer power resources, numerical methods have become an indispensable tool for the analysis of classical and quantum interacting systems. Most of these methods, such as Monte Carlo simulations, are performed at finite size systems, which demand the analysis by scaling theories to avoid misleading finite size effects [3-6]. However, depending on the type of systems (classical or quantum), or the geometry/dimensionality, performing a finite size scaling (FSS) analysis may be a challenge - sometimes an unfeasible task -, due to technical bottlenecks: for instance, as a paradigm, in quantum Monte Carlo simulations the occurrence of the infamous minus-sign problem, i.e. the occurrence a negative statistical weight, restricts the simulations to small lattice sizes [7-9]. Another instance is the analysis of three-dimensional systems, in which an extrapolation to the thermodynamic limit is very demanding, even in absence of the sign problem. In view of this, it is worth developing techniques that could give hints of the existing phases and their phase transitions at finite small system sizes, but, at the same time, could also provide quantitatively reasonable critical points. With the advent of big data analysis, e.g. with machine learning techniques, a great expectation is placed to this end. Indeed, over the past few years, there has been an effort to develop and benchmark supervised and unsupervised machine learning techniques [10-12].

I would like to start this post with the good old quote "A Picture is worth a Thousand Words". That is what Data Visualization is all about. Data Visualization is an integral part of Data Science & Data Analysis. It is not only useful for us to understand the data, but also to present the insights of the data in the form of a graphical representation which is much easier to understand. Let's say that we are working on a Data Science project.

Now let's see how to groom our data -mean making it ready so that we can feed it into our computers to get the most accurate results, this step has got a technical name -- Data Preprocessing. Data preprocessing is the modification of raw data into a more suitable form for modeling. It is used on a predictive modeling project, such as classification or regression. Machine-learning algorithms operate on numeric data. It takes numbers as input and predicts a number as output.

In simple language, the gradient descent is an ML optimization strategy which facilitates the ML model to find the minimum loss (cost) function which relates to the optimal variable parameters. Let's understand the concept in detail by applying it on one of the most regression algorithms that ML engineers and Data scientists use, that is Linear Regression. For ease of understanding Gradient descent, we will use simple or univariate linear regression. Here, we are focusing on determining the relationship between one independent variable and one dependent variable(target variable). A univariate linear regression is mathematically represented by y mx c, where'y' is the dependent variable and'x' is the independent or target variable.

A form of artificial intelligence combined with MRI scans of the brain predicted with 94% accuracy whether individuals with a specific type of early memory loss would go on to develop Alzheimer's diseases or other forms of dementia, according to a new study. University of Florida researchers studied 55 participants diagnosed with amnestic mild cognitive impairment -- a condition that is a known precursor to Alzheimer's disease and marked by signs like forgetting conversations or misplacing items. By applying a support vector machine model algorithm to a 45-minute MRI brain scan of brain structures and brain activity, researchers reported they were able to predict progression from amnestic MCI to dementia with over 94% accuracy. The algorithm delivered 92.7% accuracy when applied to a 10-minute brain scan. Fourteen participants developed dementia and 41 remained stable over a 15-month study period.

Distributional forecasts are important for a wide variety of applications, including forecasting epidemics. Often, forecasts are miscalibrated, or unreliable in assigning uncertainty to future events. We present a recalibration method that can be applied to a black-box forecaster given retrospective forecasts and observations, as well as an extension to make this method more effective in recalibrating epidemic forecasts. This method is guaranteed to improve calibration and log score performance when trained and measured in-sample. We also prove that the increase in expected log score of a recalibrated forecaster is equal to the entropy of the PIT distribution. We apply this recalibration method to the 27 influenza forecasters in the FluSight Network and show that recalibration reliably improves forecast accuracy and calibration. This method is effective, robust, and easy to use as a post-processing tool to improve epidemic forecasts.

Large-scale knowledge graphs (KGs) provide structured representations of human knowledge. However, as it is impossible to contain all knowledge, KGs are usually incomplete. Reasoning based on existing facts paves a way to discover missing facts. In this paper, we study the problem of learning logic rules for reasoning on knowledge graphs for completing missing factual triplets. Learning logic rules equips a model with strong interpretability as well as the ability to generalize to similar tasks. We propose a model called MPLR that improves the existing models to fully use training data and multi-target scenarios are considered. In addition, considering the deficiency in evaluating the performance of models and the quality of mined rules, we further propose two novel indicators to help with the problem. Experimental results empirically demonstrate that our MPLR model outperforms state-of-the-art methods on five benchmark datasets. The results also prove the effectiveness of the indicators.

The training and test data for deep-neural-network-based classifiers are usually assumed to be sampled from the same distribution. When part of the test samples are drawn from a distribution that is sufficiently far away from that of the training samples (a.k.a. out-of-distribution (OOD) samples), the trained neural network has a tendency to make high confidence predictions for these OOD samples. Detection of the OOD samples is critical when training a neural network used for image classification, object detection, etc. It can enhance the classifier's robustness to irrelevant inputs, and improve the system resilience and security under different forms of attacks. Detection of OOD samples has three main challenges: (i) the proposed OOD detection method should be compatible with various architectures of classifiers (e.g., DenseNet, ResNet), without significantly increasing the model complexity and requirements on computational resources; (ii) the OOD samples may come from multiple distributions, whose class labels are commonly unavailable; (iii) a score function needs to be defined to effectively separate OOD samples from in-distribution (InD) samples. To overcome these challenges, we propose a Wasserstein-based out-of-distribution detection (WOOD) method. The basic idea is to define a Wasserstein-distance-based score that evaluates the dissimilarity between a test sample and the distribution of InD samples. An optimization problem is then formulated and solved based on the proposed score function. The statistical learning bound of the proposed method is investigated to guarantee that the loss value achieved by the empirical optimizer approximates the global optimum. The comparison study results demonstrate that the proposed WOOD consistently outperforms other existing OOD detection methods.

We revisit the classic database of weighted-P4s which admit Calabi-Yau 3-fold hypersurfaces equipped with a diverse set of tools from the machine-learning toolbox. Unsupervised techniques identify an unanticipated almost linear dependence of the topological data on the weights. This then allows us to identify a previously unnoticed clustering in the Calabi-Yau data. Supervised techniques are successful in predicting the topological parameters of the hypersurface from its weights with an accuracy of R^2 > 95%. Supervised learning also allows us to identify weighted-P4s which admit Calabi-Yau hypersurfaces to 100% accuracy by making use of partitioning supported by the clustering behaviour.

While conventional ranking systems focus solely on maximizing the utility of the ranked items to users, fairness-aware ranking systems additionally try to balance the exposure for different protected attributes such as gender or race. To achieve this type of group fairness for ranking, we derive a new ranking system based on the first principles of distributional robustness. We formulate a minimax game between a player choosing a distribution over rankings to maximize utility while satisfying fairness constraints against an adversary seeking to minimize utility while matching statistics of the training data. We show that our approach provides better utility for highly fair rankings than existing baseline methods.