We present an unsupervised approach for discovering semantic representations of mathematical equations. Equations are challenging to analyze because each is unique, or nearly unique. Our method, which we call equation embeddings, finds good representations of equations by using the representations of their surrounding words. We used equation embeddings to analyze four collections of scientific articles from the arXiv, covering four computer science domains (NLP, IR, AI, and ML) and $\sim$98.5k equations. Quantitatively, we found that equation embeddings provide better models when compared to existing word embedding approaches. Qualitatively, we found that equation embeddings provide coherent semantic representations of equations and can capture semantic similarity to other equations and to words.

Our aim is to study gradient descent in such loss functions or energy landscapes and compare it to results obtained from real high-dimensional optimization problems such as encountered in deep learning. In particular, we analyze the distribution of the improved loss function after a step of gradient descent, provide analytic expressions for the moments as well as prove asymptotic normality as the dimension of the parameter space becomes large. Moreover, we compare this with the expectation of the global minimum of the landscape obtained by means of the Euler characteristic of excursion sets. Besides complementing our analytical findings with numerical results from simulated Gaussian random fields, we also compare it to loss functions obtained from optimisation problems on synthetic and real data sets by proposing a "black box" random field toy-model for a deep neural network loss function.

The randomized experiment is an important tool for inferring the causal impact of an intervention. The recent literature on statistical learning methods for heterogeneous treatment effects demonstrates the utility of estimating the marginal conditional average treatment effect (MCATE), i.e., the average treatment effect for a subpopulation of respondents who share a particular subset of covariates. However, each proposed method makes its own set of restrictive assumptions about the intervention's effects, the underlying data generating processes, and which subpopulations (MCATEs) to explicitly estimate. Moreover, the majority of the literature provides no mechanism to identify which subpopulations are the most affected--beyond manual inspection--and provides little guarantee on the correctness of the identified subpopulations. Therefore, we propose Treatment Effect Subset Scan (TESS), a new method for discovering which subpopulation in a randomized experiment is most significantly affected by a treatment. We frame this challenge as a pattern detection problem where we maximize a nonparametric scan statistic (measurement of distributional divergence) over subpopulations, while being parsimonious in which specific subpopulations to evaluate. Furthermore, we identify the subpopulation which experiences the largest distributional change as a result of the intervention, while making minimal assumptions about the intervention's effects or the underlying data generating process. In addition to the algorithm, we demonstrate that the asymptotic Type I and II error can be controlled, and provide sufficient conditions for detection consistency---i.e., exact identification of the affected subpopulation. Finally, we validate the efficacy of the method by discovering heterogeneous treatment effects in simulations and in real-world data from a well-known program evaluation study.

Police officers speak significantly less respectfully to black than to white community members in everyday traffic stops, even after controlling for officer race, infraction severity, stop location, and stop outcome. This paper presents a systematic analysis of officer body-worn camera footage, using computational linguistic techniques to automatically measure the respect level that officers display to community members. This work demonstrates that body camera footage can be used as a rich source of data rather than merely archival evidence, and paves the way for developing powerful language-based tools for studying and potentially improving police–community relations. Using footage from body-worn cameras, we analyze the respectfulness of police officer language toward white and black community members during routine traffic stops. We develop computational linguistic methods that extract levels of respect automatically from transcripts, informed by a thin-slicing study of participant ratings of officer utterances. We find that officers speak with consistently less respect toward black versus white community members, even after controlling for the race of the officer, the severity of the infraction, the location of the stop, and the outcome of the stop. Such disparities in common, everyday interactions between police and the communities they serve have important implications for procedural justice and the building of police–community trust. Over the last several years, our nation has been rocked by an onslaught of incidents captured on video involving police officers' use of force with black suspects.

Linear regression algorithm is used to predict the continuous valued output from a labeled training set i.e. it is a supervised learning algorithm. It is a well-known algorithm for machine learning as well as it is well-known in Statistics. If you are new to the machine learning, do read introduction to machine learning for beginners. We are having a training set of a House prediction system. We are using features of House i.e. area, the number of bedrooms, etc. as input and its price is our output.

Machine Learning (ML) is one of the most exciting and dynamic areas of modern research and application. The purpose of this review is to provide an introduction to the core concepts and tools of machine learning in a manner easily understood and intuitive to physicists. The review begins by covering fundamental concepts in ML and modern statistics such as the bias-variance tradeoff, overfitting, regularization, and generalization before moving on to more advanced topics in both supervised and unsupervised learning. Topics covered in the review include ensemble models, deep learning and neural networks, clustering and data visualization, energy-based models (including MaxEnt models and Restricted Boltzmann Machines), and variational methods. Throughout, we emphasize the many natural connections between ML and statistical physics. A notable aspect of the review is the use of Python notebooks to introduce modern ML/statistical packages to readers using physics-inspired datasets (the Ising Model and Monte-Carlo simulations of supersymmetric decays of proton-proton collisions). We conclude with an extended outlook discussing possible uses of machine learning for furthering our understanding of the physical world as well as open problems in ML where physicists maybe able to contribute. (Notebooks are available at https://physics.bu.edu/~pankajm/MLnotebooks.html )

The identification of sources of advection-diffusion transport is based usually on solving complex ill-posed inverse models against the available state- variable data records. However, if there are several sources with different locations and strengths, the data records represent mixtures rather than the separate influences of the original sources. Importantly, the number of these original release sources is typically unknown, which hinders reliability of the classical inverse-model analyses. To address this challenge, we present here a novel hybrid method for identification of the unknown number of release sources. Our hybrid method, called HNMF, couples unsupervised learning based on Nonnegative Matrix Factorization (NMF) and inverse-analysis Green functions method. HNMF synergistically performs decomposition of the recorded mixtures, finds the number of the unknown sources and uses the Green function of advection-diffusion equation to identify their characteristics. In the paper, we introduce the method and demonstrate that it is capable of identifying the advection velocity and dispersivity of the medium as well as the unknown number, locations, and properties of various sets of synthetic release sources with different space and time dependencies, based only on the recorded data. HNMF can be applied directly to any problem controlled by a partial-differential parabolic equation where mixtures of an unknown number of sources are measured at multiple locations.

Chatter identification and detection in machining processes has been an active area of research in the past two decades. Part of the challenge in studying chatter is that machining equations that describe its occurrence are often nonlinear delay differential equations. The majority of the available tools for chatter identification rely on defining a metric that captures the characteristics of chatter, and a threshold that signals its occurrence. The difficulty in choosing these parameters can be somewhat alleviated by utilizing machine learning techniques. However, even with a successful classification algorithm, the transferability of typical machine learning methods from one data set to another remains very limited. In this paper we combine supervised machine learning with Topological Data Analysis (TDA) to obtain a descriptor of the process which can detect chatter. The features we use are derived from the persistence diagram of an attractor reconstructed from the time series via Takens embedding. We test the approach using deterministic and stochastic turning models, where the stochasticity is introduced via the cutting coefficient term. Our results show a 97% successful classification rate on the deterministic model labeled by the stability diagram obtained using the spectral element method. The features gleaned from the deterministic model are then utilized for characterization of chatter in a stochastic turning model where there are very limited analysis methods.

Psychiatric neuroscience is increasingly aware of the need to define psychopathology in terms of abnormal neural computation. The central tool in this endeavour is the fitting of computational models to behavioural data. The most prominent example of this procedure is fitting reinforcement learning (RL) models to decision-making data collected from mentally ill and healthy subject populations. These models are generative models of the decision-making data themselves, and the parameters we seek to infer can be psychologically and neurobiologically meaningful. Currently, the gold standard approach to this inference procedure involves Monte-Carlo sampling, which is robust but computationally intensive---rendering additional procedures, such as cross-validation, impractical. Searching for point estimates of model parameters using optimization procedures remains a popular and interesting option. On a novel testbed simulating parameter estimation from a common RL task, we investigated the effects of smooth vs. boundary constraints on parameter estimation using interior point and deterministic direct search algorithms for optimization. Ultimately, we show that the use of boundary constraints can lead to substantial truncation effects. Our results discourage the use of boundary constraints for these applications.

A broad spectrum of data from different modalities are generated in the healthcare domain every day, including scalar data (e.g., clinical measures collected at hospitals), tensor data (e.g., neuroimages analyzed by research institutes), graph data (e.g., brain connectivity networks), and sequence data (e.g., digital footprints recorded on smart sensors). Capability for modeling information from these heterogeneous data sources is potentially transformative for investigating disease mechanisms and for informing therapeutic interventions. Our works in this thesis attempt to facilitate healthcare applications in the setting of broad learning which focuses on fusing heterogeneous data sources for a variety of synergistic knowledge discovery and machine learning tasks. We are generally interested in computer-aided diagnosis, precision medicine, and mobile health by creating accurate user profiles which include important biomarkers, brain connectivity patterns, and latent representations. In particular, our works involve four different data mining problems with application to the healthcare domain: multi-view feature selection, subgraph pattern mining, brain network embedding, and multi-view sequence prediction.