Short-term load forecasting (STLF) is essential for the reliable and economic operation of power systems. Though many STLF methods were proposed over the past decades, most of them focused on loads at high aggregation levels only. Thus, low-aggregation load forecast still requires further research and development. Compared with the substation or city level loads, individual loads are typically more volatile and much more challenging to forecast. To further address this issue, this paper first discusses the characteristics of small-and-medium enterprise (SME) and residential loads at different aggregation levels and quantifies their predictability with approximate entropy. Various STLF techniques, from the conventional linear regression to state-of-the-art deep learning, are implemented for a detailed comparative analysis to verify the forecasting performances as well as the predictability using an Irish smart meter dataset. In addition, the paper also investigates how using data processing improves individual-level residential load forecasting with low predictability. Effectiveness of the discussed method is validated with numerical results.

The present study provides a comparative assessment of non-invasive sensors as means of estimating the microbial contamination and time-on-shelf (i.e. storage time) of leafy green vegetables, using a novel unified spectra analysis workflow. Two fresh ready-to-eat green salads were used in the context of this study for the purpose of evaluating the efficiency and practical application of the presented workflow: rocket and baby spinach salads. The employed analysis workflow consisted of robust data normalization, powerful feature selection based on random forests regression, and selection of the number of partial least squares regression coefficients in the training process by estimating the knee-point on the explained variance plot. Training processes were based on microbiological and spectral data derived during storage of green salad samples at isothermal conditions (4, 8 and 12C), whereas testing was performed on data during storage under dynamic temperature conditions (simulating real-life temperature fluctuations in the food supply chain). Since an increasing interest in the use of non-invasive sensors in food quality assessment has been made evident in recent years, the unified spectra analysis workflow described herein, by being based on the creation/usage of limited sized featured sets, could be very useful in food-specific low-cost sensor development.

Heart rate estimation from electrocardiogram signals is very important for the early detection of cardiovascular diseases. However, due to large individual differences and varying electrocardiogram signal quality, there does not exist a single reliable estimation algorithm that works well on all subjects. Every algorithm may break down on certain subjects, resulting in a significant estimation error. Ensemble regression, which aggregates the outputs of multiple base estimators for more reliable and stable estimates, can be used to remedy this problem. Moreover, active learning can be used to optimally select a few trials from a new subject to label, based on which a stacking ensemble regression model can be trained to aggregate the base estimators. This paper proposes four active stacking approaches, and demonstrates that they all significantly outperform three common unsupervised ensemble regression approaches, and a supervised stacking approach which randomly selects some trials to label. Remarkably, our active stacking approaches only need three or four labeled trials from each subject to achieve an average root mean squared estimation error below three beats per minute, making them very convenient for real-world applications. To our knowledge, this is the first research on active stacking, and its application to heart rate estimation.

Cancer is one of the leading cause of death, worldwide. Many believe that genomic data will enable us to better predict the survival time of these patients, which will lead to better, more personalized treatment options and patient care. As standard survival prediction models have a hard time coping with the high-dimensionality of such gene expression (GE) data, many projects use some dimensionality reduction techniques to overcome this hurdle. We introduce a novel methodology, inspired by topic modeling from the natural language domain, to derive expressive features from the high-dimensional GE data. There, a document is represented as a mixture over a relatively small number of topics, where each topic corresponds to a distribution over the words; here, to accommodate the heterogeneity of a patient's cancer, we represent each patient (~document) as a mixture over cancer-topics, where each cancer-topic is a mixture over GE values (~words). This required some extensions to the standard LDA model eg: to accommodate the "real-valued" expression values - leading to our novel "discretized" Latent Dirichlet Allocation (dLDA) procedure. We initially focus on the METABRIC dataset, which describes breast cancer patients using the r=49,576 GE values, from microarrays. Our results show that our approach provides survival estimates that are more accurate than standard models, in terms of the standard Concordance measure. We then validate this approach by running it on the Pan-kidney (KIPAN) dataset, over r=15,529 GE values - here using the mRNAseq modality - and find that it again achieves excellent results. In both cases, we also show that the resulting model is calibrated, using the recent "D-calibrated" measure. These successes, in two different cancer types and expression modalities, demonstrates the generality, and the effectiveness, of this approach.

We discuss the relevance of the recent Machine Learning (ML) literature for economics and econometrics. First we discuss the differences in goals, methods and settings between the ML literature and the traditional econometrics and statistics literatures. Then we discuss some specific methods from the machine learning literature that we view as important for empirical researchers in economics. These include supervised learning methods for regression and classification, unsupervised learning methods, as well as matrix completion methods. Finally, we highlight newly developed methods at the intersection of ML and econometrics, methods that typically perform better than either off-the-shelf ML or more traditional econometric methods when applied to particular classes of problems, problems that include causal inference for average treatment effects, optimal policy estimation, and estimation of the counterfactual effect of price changes in consumer choice models.

Linear regression is the most basic and the most widely used technique in machine learning; yet for all its simplicity, studying it can unlock some of the most important concepts in statistics. If you have a basic undestanding of linear regression expressed as $ \hat{Y} \theta_0 \theta_1X$, but don't have a background in statistics and find statements like "ridge regression is equivalent to the maximum a posteriori (MAP) estimate with a zero-mean Gaussian prior" bewildering, then this post is for you. With a superficial goal of understanding that somewhat obtuse statement, its main objective is to explore the topic, starting from the standard formulation of linear regression, moving on to the probabilistic approach (maximum likelihood formulation) and from there to Bayesian linear regression. I'll use the $\theta$ character throughout to refer to the coefficients (weights) of a regression model, either explicitly broken out as $\theta_0$ and $\theta_1$ for intercept and slope respectively, or just $\theta$ referring to the vector of coefficients. I'll usually use the expression $\theta Tx_i$ for the prediction a model gives at $x_i$, the assumption being that a 1 has been added to the vector of values at $x_i$. 1 In the single predictor case, we know that the least squares fit is the line that minimizes the sum of the squared distances between observed data and predicted values, i.e. it minimizes the Residual Sum of Squares (RSS): These residuals are pretty important in how we reason about our model.

The paper studies binary classification and aims at estimating the underlying regression function which is the conditional expectation of the class labels given the inputs. The regression function is the key component of the Bayes optimal classifier, moreover, besides providing optimal predictions, it can also assess the risk of misclassification. We aim at building non-asymptotic confidence regions for the regression function and suggest three kernel-based semi-parametric resampling methods. We prove that all of them guarantee regions with exact coverage probabilities and they are strongly consistent.

Reinforcement learning algorithms can be used to optimally solve dynamic decision-making and control problems. With continuous-valued state and input variables, reinforcement learning algorithms must rely on function approximators to represent the value function and policy mappings. Commonly used numerical approximators, such as neural networks or basis function expansions, have two main drawbacks: they are black-box models offering no insight in the mappings learned, and they require significant trial and error tuning of their meta-parameters. In this paper, we propose a new approach to constructing smooth value functions by means of symbolic regression. We introduce three off-line methods for finding value functions based on a state transition model: symbolic value iteration, symbolic policy iteration, and a direct solution of the Bellman equation. The methods are illustrated on four nonlinear control problems: velocity control under friction, one-link and two-link pendulum swing-up, and magnetic manipulation. The results show that the value functions not only yield well-performing policies, but also are compact, human-readable and mathematically tractable. This makes them potentially suitable for further analysis of the closed-loop system. A comparison with alternative approaches using neural networks shows that our method constructs well-performing value functions with substantially fewer parameters.

We consider Hadamard product parametrization as a change-of-variable (over-parametrization) technique for solving least square problems in the context of linear regression. Despite the non-convexity and exponentially many saddle points induced by the change-of-variable, we show that under certain conditions, this over-parametrization leads to implicit regularization: if we directly apply gradient descent to the residual sum of squares with sufficiently small initial values, then under proper early stopping rule, the iterates converge to a nearly sparse rate-optimal solution with relatively better accuracy than explicit regularized approaches. In particular, the resulting estimator does not suffer from extra bias due to explicit penalties, and can achieve the parametric root-$n$ rate (independent of the dimension) under proper conditions on the signal-to-noise ratio. We perform simulations to compare our methods with high dimensional linear regression with explicit regularizations. Our results illustrate advantages of using implicit regularization via gradient descent after over-parametrization in sparse vector estimation.

We consider {\em Mixed Linear Regression (MLR)}, where training data have been generated from a mixture of distinct linear models (or clusters) and we seek to identify the corresponding coefficient vectors. We introduce a {\em Mixed Integer Programming (MIP)} formulation for MLR subject to regularization constraints on the coefficient vectors. We establish that as the number of training samples grows large, the MIP solution converges to the true coefficient vectors in the absence of noise. Subject to slightly stronger assumptions, we also establish that the MIP identifies the clusters from which the training samples were generated. In the special case where training data come from a single cluster, we establish that the corresponding MIP yields a solution that converges to the true coefficient vector even when training data are perturbed by (martingale difference) noise. We provide a counterexample indicating that in the presence of noise, the MIP may fail to produce the true coefficient vectors for more than one clusters. We also provide numerical results testing the MIP solutions in synthetic examples with noise.