We study the forecasting of the power consumptions of a population of households and of subpopulations thereof. These subpopulations are built according to location, to exogenous information and/or to profiles we determined from historical households consumption time series. Thus, we aim to forecast the electricity consumption time series at several levels of households aggregation. These time series are linked through some summation constraints which induce a hierarchy. Our approach consists in three steps: feature generation, aggregation and projection. Firstly (feature generation step), we build, for each considering group for households, a benchmark forecast (called features), using random forests or generalized additive models. Secondly (aggregation step), aggregation algorithms, run in parallel, aggregate these forecasts and provide new predictions. Finally (projection step), we use the summation constraints induced by the time series underlying hierarchy to re-conciliate the forecasts by projecting them in a well-chosen linear subspace. We provide some theoretical guaranties on the average prediction error of this methodology, through the minimization of a quantity called regret. We also test our approach on households power consumption data collected in Great Britain by multiple energy providers in the Energy Demand Research Project context. We build and compare various population segmentations for the evaluation of our approach performance.

Have you ever asked yourself a series of questions in order to help make a final decision on something? Maybe it was a simple decision like what you wanted to eat for dinner. You might have asked yourself if you wanted to cook or pick food up or get delivery. If you decided to cook, then you would have needed to figure out what type of cuisine you were in the mood for. And lastly, you probably needed to figure out if you had all of the ingredients in your fridge or needed to make a run to the store.

In this video, we will discuss practical considerations in designing a decision tree model. We will discuss how to overcome overfitting in decision trees, three ways to prune the tree, and how to handle missing attributes and continuous values. This channel is part of CSEdu4All, an educational initiative that aims to make computer science education accessible to all! We believe that everyone has the right to good education, and geographical and political boundaries should not be a barrier to obtaining knowledge and information. We hope that you will join and support us in this endeavor!

We consider the use of decision trees for decision-making problems under the predict-then-optimize framework. That is, we would like to first use a decision tree to predict unknown input parameters of an optimization problem, and then make decisions by solving the optimization problem using the predicted parameters. A natural loss function in this framework is to measure the suboptimality of the decisions induced by the predicted input parameters, as opposed to measuring loss using input parameter prediction error. This natural loss function is known in the literature as the Smart Predict-then-Optimize (SPO) loss, and we propose a tractable methodology called SPO Trees (SPOTs) for training decision trees under this loss. SPOTs benefit from the interpretability of decision trees, providing an interpretable segmentation of contextual features into groups with distinct optimal solutions to the optimization problem of interest. We conduct several numerical experiments on synthetic and real data including the prediction of travel times for shortest path problems and predicting click probabilities for news article recommendation. We demonstrate on these datasets that SPOTs simultaneously provide higher quality decisions and significantly lower model complexity than other machine learning approaches (e.g., CART) trained to minimize prediction error.

We present a general architecture of deep differentiable forest and its sparse attention mechanism. The differentiable forest has the advantages of both trees and neural networks. Its structure is a simple binary tree, easy to use and understand. It has full differentiability and all variables are learnable parameters. We would train it by the gradient-based optimization method, which shows great power in the training of deep CNN. We find and analyze the attention mechanism in the differentiable forest. That is, each decision depends on only a few important features, and others are irrelevant. The attention is always sparse. Based on this observation, we improve its sparsity by data-aware initialization. We use the attribute importance to initialize the attention weight. Then the learned weight is much sparse than that from random initialization. Our experiment on some large tabular dataset shows differentiable forest has higher accuracy than GBDT, which is the state of art algorithm for tabular datasets. The source codes are available at https://github.com/closest-git/QuantumForest

There is little argument about whether or not machine learning models are useful for applying to social systems. But if we take seriously George Box's dictum, or indeed the even older one that "the map is not the territory' (Korzybski, 1933), then there has been comparatively less systematic attention paid within the field to how machine learning models are wrong (Selbst et al., 2019) and seeing possible harms in that light. By "wrong" I do not mean in terms of making misclassifications, or even fitting over the'wrong' class of functions, but more fundamental mathematical/statistical assumptions, philosophical (in the sense used by Abbott, 1988) commitments about how we represent the world, and sociological processes of how models interact with target phenomena. This paper takes a particular model of machine learning research or application: one that its creators and deployers think provides a reliable way of interacting with the social world (whether that is through understanding, or in making predictions) without any intent to cause harm (McQuillan, 2018) and, in fact, a desire to not cause harm and instead improve the world, 1 for example as most explicitly in the various "{Data [Science], Machine Learning, Artificial Intelligence} for [Social] Good" initiatives, and more widely in framings around "fairness" or "ethics." I focus on the almost entirely statistical modern version of machine learning, rather than eclipsed older visions (see section 3). While many of the limitations I discuss apply to the use of machine learning in any domain, I focus on applications to the social world in order to explore the domain where limitations are strongest and stickiest.

By Clare Liu, Data Scientist at fintech industry, based in HK. A decision tree is one of the popular and powerful machine learning algorithms that I have learned. It is a non-parametric supervised learning method that can be used for both classification and regression tasks. The goal is to create a model that predicts the value of a target variable by learning simple decision rules inferred from the data features. For a classification model, the target values are discrete in nature, whereas, for a regression model, the target values are represented by continuous values.

A key assumption in multiple scientific applications is that the distribution of observed data can be modeled by a latent tree graphical model. An important example is phylogenetics, where the tree models the evolutionary lineages of various organisms. Given a set of independent realizations of the random variables at the leaves of the tree, a common task is to infer the underlying tree topology. In this work we develop Spectral Neighbor Joining (SNJ), a novel method to recover latent tree graphical models. In contrast to distance based methods, SNJ is based on a spectral measure of similarity between all pairs of observed variables. We prove that SNJ is consistent, and derive a sufficient condition for correct tree recovery from an estimated similarity matrix. Combining this condition with a concentration of measure result on the similarity matrix, we bound the number of samples required to recover the tree with high probability. We illustrate via extensive simulations that SNJ requires fewer samples to accurately recover trees in regimes where the tree contains a large number of leaves or long edges. We provide theoretical support for this observation by analyzing the model of a perfect binary tree.

Clustering is a popular form of unsupervised learning for geometric data. Unfortunately, many clustering algorithms lead to cluster assignments that are hard to explain, partially because they depend on all the features of the data in a complicated way. To improve interpretability, we consider using a small decision tree to partition a data set into clusters, so that clusters can be characterized in a straightforward manner. We study this problem from a theoretical viewpoint, measuring cluster quality by the $k$-means and $k$-medians objectives: Must there exist a tree-induced clustering whose cost is comparable to that of the best unconstrained clustering, and if so, how can it be found? In terms of negative results, we show, first, that popular top-down decision tree algorithms may lead to clusterings with arbitrarily large cost, and second, that any tree-induced clustering must in general incur an $\Omega(\log k)$ approximation factor compared to the optimal clustering. On the positive side, we design an efficient algorithm that produces explainable clusters using a tree with $k$ leaves. For two means/medians, we show that a single threshold cut suffices to achieve a constant factor approximation, and we give nearly-matching lower bounds. For general $k \geq 2$, our algorithm is an $O(k)$ approximation to the optimal $k$-medians and an $O(k^2)$ approximation to the optimal $k$-means. Prior to our work, no algorithms were known with provable guarantees independent of dimension and input size.

Today, machine learning (ML) models are increasingly applied in decision making. This induces an urgent need for quality assurance of ML models with respect to (often domain-dependent) requirements. Monotonicity is one such requirement. It specifies a software as 'learned' by an ML algorithm to give an increasing prediction with the increase of some attribute values. While there exist multiple ML algorithms for ensuring monotonicity of the generated model, approaches for checking monotonicity, in particular of black-box models, are largely lacking. In this work, we propose verification-based testing of monotonicity, i.e., the formal computation of test inputs on a white-box model via verification technology, and the automatic inference of this approximating white-box model from the black-box model under test. On the white-box model, the space of test inputs can be systematically explored by a directed computation of test cases. The empirical evaluation on 90 black-box models shows verification-based testing can outperform adaptive random testing as well as property-based techniques with respect to effectiveness and efficiency.