Purpose: To utilize high-resolution quantitative CT (QCT) imaging features for prediction of diagnosis and prognosis in fibrosing interstitial lung diseases (ILD). Approach: 40 ILD patients (20 usual interstitial pneumonia (UIP), 20 non-UIP pattern ILD) were classified by expert consensus of 2 radiologists and followed for 7 years. Clinical variables were recorded. Following segmentation of the lung field, a total of 26 texture features were extracted using a lattice-based approach (TM model). The TM model was compared with previously histogram-based model (HM) for their abilities to classify UIP vs non-UIP. For prognostic assessment, survival analysis was performed comparing the expert diagnostic labels versus TM metrics. Results: In the classification analysis, the TM model outperformed the HM method with AUC of 0.70. While survival curves of UIP vs non-UIP expert labels in Cox regression analysis were not statistically different, TM QCT features allowed statistically significant partition of the cohort. Conclusions: TM model outperformed HM model in distinguishing UIP from non-UIP patterns. Most importantly, TM allows for partitioning of the cohort into distinct survival groups, whereas expert UIP vs non-UIP labeling does not. QCT TM models may improve diagnosis of ILD and offer more accurate prognostication, better guiding patient management.

We develop a computational procedure to estimate the covariance hyperparameters for semiparametric Gaussian process regression models with additive noise. Namely, the presented method can be used to efficiently estimate the variance of the correlated error, and the variance of the noise based on maximizing a marginal likelihood function. Our method involves suitably reducing the dimensionality of the hyperparameter space to simplify the estimation procedure to a univariate root-finding problem. Moreover, we derive bounds and asymptotes of the marginal likelihood function and its derivatives, which are useful to narrowing the initial range of the hyperparameter search. Using numerical examples, we demonstrate the computational advantages and robustness of the presented approach compared to traditional parameter optimization.

Since the start of your data scientist journey, you have been commonly accustomed with this machine learning algorithm. Linear Regression as it is the basic and foremost machine learning algorithm we generally start with while analysing different regression problems. As the word linear says, the linear relationship between input variables(x) with the dependent output variable(y). Basically the linear regression analysis performs the task of predicticting the output variable by modelling or finding relationships between the independent variables(x). And the approach of finding the best ouput is by fitting the predicted line towards the best fit line.

It is possible to design and deploy advanced machine learning algorithms that are essentially math-free and stats-free. People working on that are typically professional mathematicians. These algorithms are not necessarily simpler. See for instance a math-free regression technique with prediction intervals, here. Or supervised classification and alternative to t-SNE, here. Interestingly, this latter math-free machine

As described by each words Linear (arranged in or extending along a straight or nearly straight line) Regression (measure of the relation between variables). Linear Regression attempts to model the relationship between two variables by fitting a linear equation to observed data. One variable is considered to be an explanatory variable, or features, and the other is considered to be a dependent variable, or target. In the field of machine learning Linear Regression is a considered a supervised learning task. A Linear Regression line has an equation of the form Y mX C, where X is the explanatory variable or feature variable and Y is the dependent variable or a target variable.

The volume of a lake is a crucial component in understanding environmental and hydrologic processes. The State of Minnesota (USA) has tens of thousands of lakes, but only a small fraction has readily available bathymetric information. In this paper we develop and test methods for predicting water volume in the lake-rich region of Central Minnesota. We used three different published regression models for predicting lake volume using available data. The first model utilized lake surface area as the sole independent variable. The second model utilized lake surface area but also included an additional independent variable, the average change in land surface area in a designated buffer area surrounding a lake. The third model also utilized lake surface area but assumed the land surface to be a self-affine surface, thus allowing the surface area-lake volume relationship to be governed by a scale defined by the Hurst coefficient. These models all utilized bathymetric data available for 816 lakes across the region of study. The models explained over 80% of the variation in lake volumes. The sum difference between the total predicted lake volume and known volumes were <2%. We applied these models to predicting lake volumes using available independent variables for over 40,000 lakes within the study region. The total lake volumes for the methods ranged from 1,180,000- and 1,200,000-hectare meters. We also investigated machine learning models for estimating the individual lake volume...

Andrew Ng's DeepLearning.AI, in partnership with Stanford Online, recently announced a new Machine Learning Specialisation course on Coursera. This beginner-friendly program will teach you the fundamentals of machine learning and how to use these techniques to build real-world AI applications. The 3-course program is a new version of Ng's pioneering machine learning course, taken by over 4.8 million learners since 2012. The program provides a broad introduction to modern machine learning, including supervised learning (multiple linear regression, logistic regression, neural networks, and decision trees), unsupervised learning (clustering, dimensionality reduction, recommender systems), and some of the best practices used in Silicon Valley for artificial intelligence and machine learning innovation. The new Machine Learning Specialization by @DeepLearningAI_ & @StanfordOnline is now available on @Coursera!

Classifying samples in incomplete datasets is a common aim for machine learning practitioners, but is non-trivial. Missing data is found in most real-world datasets and these missing values are typically imputed using established methods, followed by classification of the now complete, imputed, samples. The focus of the machine learning researcher is then to optimise the downstream classification performance. In this study, we highlight that it is imperative to consider the quality of the imputation. We demonstrate how the commonly used measures for assessing quality are flawed and propose a new class of discrepancy scores which focus on how well the method recreates the overall distribution of the data. To conclude, we highlight the compromised interpretability of classifier models trained using poorly imputed data. All code and data used in this paper are also released publicly at [inserted upon publication].

We consider the robust linear regression model $\boldsymbol{y} = X\beta^* + \boldsymbol{\eta}$, where an adversary oblivious to the design $X \in \mathbb{R}^{n \times d}$ may choose $\boldsymbol{\eta}$ to corrupt all but a (possibly vanishing) fraction of the observations $\boldsymbol{y}$ in an arbitrary way. Recent work [dLN+21, dNS21] has introduced efficient algorithms for consistent recovery of the parameter vector. These algorithms crucially rely on the design matrix being well-spread (a matrix is well-spread if its column span is far from any sparse vector). In this paper, we show that there exists a family of design matrices lacking well-spreadness such that consistent recovery of the parameter vector in the above robust linear regression model is information-theoretically impossible. We further investigate the average-case time complexity of certifying well-spreadness of random matrices. We show that it is possible to efficiently certify whether a given $n$-by-$d$ Gaussian matrix is well-spread if the number of observations is quadratic in the ambient dimension. We complement this result by showing rigorous evidence -- in the form of a lower bound against low-degree polynomials -- of the computational hardness of this same certification problem when the number of observations is $o(d^2)$.

We examine the necessity of interpolation in overparameterized models, that is, when achieving optimal predictive risk in machine learning problems requires (nearly) interpolating the training data. In particular, we consider simple overparameterized linear regression $y = X \theta + w$ with random design $X \in \mathbb{R}^{n \times d}$ under the proportional asymptotics $d/n \to \gamma \in (1, \infty)$. We precisely characterize how prediction (test) error necessarily scales with training error in this setting. An implication of this characterization is that as the label noise variance $\sigma^2 \to 0$, any estimator that incurs at least $\mathsf{c}\sigma^4$ training error for some constant $\mathsf{c}$ is necessarily suboptimal and will suffer growth in excess prediction error at least linear in the training error. Thus, optimal performance requires fitting training data to substantially higher accuracy than the inherent noise floor of the problem.