The Regression Tree (RT) sorts the samples using a specific feature and finds the split point that produces the maximum variance reduction from a node to its children. Our key observation is that the best factor to use (in terms of MSE drop) is always the target itself, as this most clearly separates the target. Thus using the target as the splitting factor provides an upper bound on MSE drop (or lower bound on the residual children MSE). Based on this observation, we define the k-bit lepto-variance ${\lambda}k^2$ of a target variable (or equivalently the lepto-variance at a specific depth k) as the variance that cannot be removed by any regression tree of a depth equal to k. As the upper bound performance for any feature, we believe ${\lambda}k^2$ to be an interesting statistical concept related to the underlying structure of the sample as it quantifies the resolving power of the RT for the sample. The max variance that may be explained using RTs of depth up to k is called the sample k-bit macro-variance. At any depth, total sample variance is thus decomposed into lepto-variance ${\lambda}^2$ and macro-variance ${\mu}^2$. We demonstrate the concept, by performing 1- and 2-bit RT based lepto-structure analysis for daily IBM stock returns.

Classification ensemble models are those composed by many models fitted to the same data, where the result for the classification can be the majority's vote, an average of the results, or the best performing model result. In Figure 1, there is an example of the voting classifier that we are going to build in this quick tutorial. Observe that there are three models fitted to the data. Two of them classified the data as 1, while one classified as 0. So, by the majority's vote, class 1 wins, and that is the result. In Scikit-Learn, a commonly used example of ensemble model is the Random Forest classifier.

Machine learning is a really interesting concept in computer programming. It involves using data to train a computer program to carry out tasks. During the process, the program learns from data by discovering patterns. This reduces the need for programmers to hard code rules in some applications. Languages like Python and R are excellent for learning and carrying out machine learning tasks.

We establish new hardness results for decision tree optimization problems, adding to a line of work that dates back to Hyafil and Rivest in 1976. We prove, under randomized ETH, superpolynomial lower bounds for two basic problems: given an explicit representation of a function $f$ and a generator for a distribution $\mathcal{D}$, construct a small decision tree approximator for $f$ under $\mathcal{D}$, and decide if there is a small decision tree approximator for $f$ under $\mathcal{D}$. Our results imply new lower bounds for distribution-free PAC learning and testing of decision trees, settings in which the algorithm only has restricted access to $f$ and $\mathcal{D}$. Specifically, we show: $n$-variable size-$s$ decision trees cannot be properly PAC learned in time $n^{\tilde{O}(\log\log s)}$, and depth-$d$ decision trees cannot be tested in time $\exp(d^{\,O(1)})$. For learning, the previous best lower bound only ruled out $\text{poly}(n)$-time algorithms (Alekhnovich, Braverman, Feldman, Klivans, and Pitassi, 2009). For testing, recent work gives similar though incomparable bounds in the setting where $f$ is random and $\mathcal{D}$ is nonexplicit (Blais, Ferreira Pinto Jr., and Harms, 2021). Assuming a plausible conjecture on the hardness of Set-Cover, we show our lower bound for learning decision trees can be improved to $n^{\Omega(\log s)}$, matching the best known upper bound of $n^{O(\log s)}$ due to Ehrenfeucht and Haussler (1989). We obtain our results within a unified framework that leverages recent progress in two lines of work: the inapproximability of Set-Cover and XOR lemmas for query complexity. Our framework is versatile and yields results for related concept classes such as juntas and DNF formulas.

New models of the attention-based random forests called LARF (Leaf Attention-based Random Forest) are proposed. The first idea behind the models is to introduce a two-level attention, where one of the levels is the "leaf" attention and the attention mechanism is applied to every leaf of trees. The second level is the tree attention depending on the "leaf" attention. The second idea is to replace the softmax operation in the attention with the weighted sum of the softmax operations with different parameters. It is implemented by applying a mixture of the Huber's contamination models and can be regarded as an analog of the multi-head attention with "heads" defined by selecting a value of the softmax parameter. Attention parameters are simply trained by solving the quadratic optimization problem. To simplify the tuning process of the models, it is proposed to make the tuning contamination parameters to be training and to compute them by solving the quadratic optimization problem. Many numerical experiments with real datasets are performed for studying LARFs. The code of proposed algorithms can be found in https://github.com/andruekonst/leaf-attention-forest.

With the advancement of technology for artificial intelligence (AI) based solutions and analytics compute engines, machine learning (ML) models are getting more complex day by day. Most of these models are generally used as a black box without user interpretability. Such complex ML models make it more difficult for people to understand or trust their predictions. There are variety of frameworks using explainable AI (XAI) methods to demonstrate explainability and interpretability of ML models to make their predictions more trustworthy. In this manuscript, we propose a methodology that we define as Local Interpretable Model Agnostic Shap Explanations (LIMASE). This proposed ML explanation technique uses Shapley values under the LIME paradigm to achieve the following (a) explain prediction of any model by using a locally faithful and interpretable decision tree model on which the Tree Explainer is used to calculate the shapley values and give visually interpretable explanations.

Governments have to supervise and inspect social economy enterprises (SEEs). However, inspecting all SEEs is not possible due to the large number of SEEs and the low number of inspectors in general. We proposed a prediction model based on a machine learning approach. The method was trained with the random forest algorithm with historical data provided by each SEE. Three consecutive periods of data were concatenated. The proposed method uses these periods as input data and predicts the risk of each SEE in the fourth period. The model achieved 76\% overall accuracy. In addition, it obtained good accuracy in predicting the high risk of a SEE. We found that the legal nature and the variation of the past-due portfolio are good predictors of the future risk of a SEE. Thus, the risk of a SEE in a future period can be predicted by a supervised machine learning method. Predicting the high risk of a SEE improves the daily work of each inspector by focusing only on high-risk SEEs.

Out of Bag (OOB) Evaluation is a very important yet underrated topic in ensemble learning. People tend to learn a lot about Random forests and other bagging algorithms, but often they tend to skip or overlook this concept. I myself missed it while learning about ensemble models and failed an interview where the last question asked was "How are the Out of Bag data utilized while training a random forest model?" (hence, decided to write this blog as a lesson) Oops! Cannot recall random forests? Basically, it is nothing but absolute supervised learning based on the concept of creating independent base learners (multiple decision trees containing bootstrapped samples from the original dataset) and training them. The bootstrapped samples are created by random sampling with replacement of dataset(d), with n features, where each sample d is less than d, and n n.

There is great demand for scalable, secure, and efficient privacy-preserving machine learning models that can be trained over distributed data. While deep learning models typically achieve the best results in a centralized non-secure setting, different models can excel when privacy and communication constraints are imposed. Instead, tree-based approaches such as XGBoost have attracted much attention for their high performance and ease of use; in particular, they often achieve state-of-the-art results on tabular data. Consequently, several recent works have focused on translating Gradient Boosted Decision Tree (GBDT) models like XGBoost into federated settings, via cryptographic mechanisms such as Homomorphic Encryption (HE) and Secure Multi-Party Computation (MPC). However, these do not always provide formal privacy guarantees, or consider the full range of hyperparameters and implementation settings. In this work, we implement the GBDT model under Differential Privacy (DP). We propose a general framework that captures and extends existing approaches for differentially private decision trees. Our framework of methods is tailored to the federated setting, and we show that with a careful choice of techniques it is possible to achieve very high utility while maintaining strong levels of privacy.

Internet of Things (IoT) devices are progressively being utilised in a variety of edge applications to monitor and control home and industry infrastructure. Due to the limited compute and energy resources, active security protections are usually minimal in many IoT devices. This has created a critical security challenge that has attracted researchers' attention in the field of network security. Despite a large number of proposed Network Intrusion Detection Systems (NIDSs), there is limited research into practical IoT implementations, and to the best of our knowledge, no edge-based NIDS has been demonstrated to operate on common low-power chipsets found in the majority of IoT devices, such as the ESP8266. This research aims to address this gap by pushing the boundaries on low-power Machine Learning (ML) based NIDSs. We propose and develop an efficient and low-power ML-based NIDS, and demonstrate its applicability for IoT edge applications by running it on a typical smart light bulb. We also evaluate our system against other proposed edge-based NIDSs and show that our model has a higher detection performance, and is significantly faster and smaller, and therefore more applicable to a wider range of IoT edge devices.