There is an increasing interest in and demand for interpretations and explanations of machine learning models and predictions in various application areas. In this paper, we consider data-driven models which are already developed, implemented and trained. Our goal is to interpret the models and explain and understand their predictions. Since the predictions made by data-driven models rely heavily on the data used for training, we believe explanations should convey information about how the training data affects the predictions. To do this, we propose a novel methodology which we call Shapley values for training data subset importance. The Shapley value concept originates from coalitional game theory, developed to fairly distribute the payout among a set of cooperating players. We extend this to subset importance, where a prediction is explained by treating the subsets of the training data as players in a game where the predictions are the payouts. We describe and illustrate how the proposed method can be useful and demonstrate its capabilities on several examples. We show how the proposed explanations can be used to reveal biasedness in models and erroneous training data. Furthermore, we demonstrate that when predictions are accurately explained in a known situation, then explanations of predictions by simple models correspond to the intuitive explanations. We argue that the explanations enable us to perceive more of the inner workings of the algorithms, and illustrate how models producing similar predictions can be based on very different parts of the training data. Finally, we show how we can use Shapley values for subset importance to enhance our training data acquisition, and by this reducing prediction error.

In the machine learning algorithms, the choice of the hyperparameter is often an art more than a science, requiring labor-intensive search with expert experience. Therefore, automation on hyperparameter optimization to exclude human intervention is a great appeal, especially for the black-box functions. Recently, there have been increasing demands of solving such concealed tasks for better generalization, though the task-dependent issue is not easy to solve. The Black-Box Optimization challenge (NeurIPS 2020) required competitors to build a robust black-box optimizer across different domains of standard machine learning problems. This paper describes the approach of team KAIST OSI in a step-wise manner, which outperforms the baseline algorithms by up to +20.39%. We first strengthen the local Bayesian search under the concept of region reliability. Then, we design a combinatorial kernel for a Gaussian process kernel. In a similar vein, we combine the methodology of Bayesian and multi-armed bandit,(MAB) approach to select the values with the consideration of the variable types; the real and integer variables are with Bayesian, while the boolean and categorical variables are with MAB. Empirical evaluations demonstrate that our method outperforms the existing methods across different tasks.

In the resource management of wireless networks, Federated Learning has been used to predict handovers. However, non-independent and identically distributed data degrade the accuracy performance of such predictions. To overcome the problem, Federated Learning can leverage data clustering algorithms and build a machine learning model for each cluster. However, traditional data clustering algorithms, when applied to the handover prediction, exhibit three main limitations: the risk of data privacy breach, the fixed shape of clusters, and the non-adaptive number of clusters. To overcome these limitations, in this paper, we propose a three-phased data clustering algorithm, namely: generative adversarial network-based clustering, cluster calibration, and cluster division. We show that the generative adversarial network-based clustering preserves privacy. The cluster calibration deals with dynamic environments by modifying clusters. Moreover, the divisive clustering explores the different number of clusters by repeatedly selecting and dividing a cluster into multiple clusters. A baseline algorithm and our algorithm are tested on a time series forecasting task. We show that our algorithm improves the performance of forecasting models, including cellular network handover, by 43%.

This course teaches you about one popular technique used in machine learning, data science and statistics: linear regression. We cover the theory from

Machine Learning is making huge leaps forward, with an increasing number of algorithms enabling us to solve complex real-world problems. This story is part of a deep dive series explaining the mechanics of Machine Learning algorithms. In addition to giving you an understanding of how ML algorithms work, it also provides you with Python examples to build your own ML models. Locally Weighted Scatterplot Smoothing sits within the family of regression algorithms under the umbrella of Supervised Learning. This means that you need a set of labeled data with a numerical target variable to train your model.

The nuclear norm and Schatten-$p$ quasi-norm of a matrix are popular rank proxies in low-rank matrix recovery. Unfortunately, computing the nuclear norm or Schatten-$p$ quasi-norm of a tensor is NP-hard, which is a pity for low-rank tensor completion (LRTC) and tensor robust principal component analysis (TRPCA). In this paper, we propose a new class of rank regularizers based on the Euclidean norms of the CP component vectors of a tensor and show that these regularizers are monotonic transformations of tensor Schatten-$p$ quasi-norm. This connection enables us to minimize the Schatten-$p$ quasi-norm in LRTC and TRPCA implicitly. The methods do not use the singular value decomposition and hence scale to big tensors. Moreover, the methods are not sensitive to the choice of initial rank and provide an arbitrarily sharper rank proxy for low-rank tensor recovery compared to nuclear norm. We provide theoretical guarantees in terms of recovery error for LRTC and TRPCA, which show relatively smaller $p$ of Schatten-$p$ quasi-norm leads to tighter error bounds. Experiments using LRTC and TRPCA on synthetic data and natural images verify the effectiveness and superiority of our methods compared to baseline methods.

One way to understand how the brain adapts to its environment is to view it as a type of generative pattern-creation model [20], one that is engaged in a never-ending process of self-correction, often without external teaching signals (or labels) [53]. Under this perspective, the brain is continuously making predictions about elements of its environment, a process that allows it to infer useful representations of the sensory data it receives [56] as well as to synthesize novel patterns, which could serve as the potential basis for long-term planning and imagination itself [12]. From the theoretical viewpoint of predictive processing, the brain could be likened to a hierarchical model whose levels are implemented by neurons (or clusters of neurons). If levels are likened to regions of the brain, the neurons at one level (region) attempt to predict the state of neurons at another level (region) and adjust/correct their local model synaptic parameters based on how different their predictions were from the observed signal. Furthermore, these neurons utilize various mechanisms to laterally stimulate/suppress each other [40] to facilitate contextual processing (such as grouping/segmenting visual components of objects in a scene).

Research in machine learning has successfully developed algorithms to build accurate classification models. However, in many real-world applications, such as healthcare, customer satisfaction, and environment protection, we want to be able to use the models to decide what actions to take. We investigate the concept of actionability in the context of Support Vector Machines. Actionability is as important as interpretability or explainability of machine learning models, an ongoing and important research topic. Actionability is the task that gives us ways to act upon machine learning models and their predictions. This paper finds a solution to the question of actionability on both linear and non-linear SVM models. Additionally, we introduce a way to account for weighted actions that allow for more change in certain features than others. We propose a gradient descent solution on the linear, RBF, and polynomial kernels, and we test the effectiveness of our models on both synthetic and real datasets. We are also able to explore the model's interpretability through the lens of actionability.

Can we learn how to explore unknown spaces efficiently? To answer this question, we study the problem of Online Graph Exploration, the online version of the Traveling Salesperson Problem. We reformulate graph exploration as a reinforcement learning problem and apply Direct Future Prediction (Dosovitskiy and Koltun, 2016) to solve it. As the graph is discovered online, the corresponding Markov Decision Process entails a dynamic state space, namely the observable graph and a dynamic action space, namely the nodes forming the graph's frontier. To the best of our knowledge, this is the first attempt to solve online graph exploration in a data-driven way. We conduct experiments on six data sets of procedurally generated graphs and three real city road networks. We demonstrate that our agent can learn strategies superior to many well known graph traversal algorithms, confirming that exploration can be learned.

Albeit worryingly underrated in the recent literature on machine learning in general (and, on deep learning in particular), multivariate density estimation is a fundamental task in many applications, at least implicitly, and still an open issue. With a few exceptions, deep neural networks (DNNs) have seldom been applied to density estimation, mostly due to the unsupervised nature of the estimation task, and (especially) due to the need for constrained training algorithms that ended up realizing proper probabilistic models that satisfy Kolmogorov's axioms. Moreover, in spite of the well-known improvement in terms of modeling capabilities yielded by mixture models over plain single-density statistical estimators, no proper mixtures of multivariate DNN-based component densities have been investigated so far. The paper fills this gap by extending our previous work on Neural Mixture Densities (NMMs) to multivariate DNN mixtures. A maximum-likelihood (ML) algorithm for estimating Deep NMMs (DNMMs) is handed out, which satisfies numerically a combination of hard and soft constraints aimed at ensuring satisfaction of Kolmogorov's axioms. The class of probability density functions that can be modeled to any degree of precision via DNMMs is formally defined. A procedure for the automatic selection of the DNMM architecture, as well as of the hyperparameters for its ML training algorithm, is presented (exploiting the probabilistic nature of the DNMM). Experimental results on univariate and multivariate data are reported on, corroborating the effectiveness of the approach and its superiority to the most popular statistical estimation techniques.