In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Ex Input:
In classical machine learning, regression is treated as a black box process of identifying a suitable function from a hypothesis set without attempting to gain insight into the mechanism connecting inputs and outputs. In the natural sciences, however, finding an interpretable function for a phenomenon is the prime goal as it allows to understand and generalize results. This paper proposes a novel type of function learning network, called equation learner (EQL), that can learn analytical expressions and is able to extrapolate to unseen domains. It is implemented as an end-to-end differentiable feed-forward network and allows for efficient gradient based training. Due to sparsity regularization concise interpretable expressions can be obtained. Often the true underlying source expression is identified. INTRODUCTION The quality of a model is typically measured by its ability to generalize from a training set to previously unseen data from the same distribution. In regression tasks generalization essentially boils down to interpolation if the training data is sufficiently dense. As long as models are selected correctly, i. e. in a way to not overfit the data, the regression problem is well understood and can – at least conceptually – be considered solved. However, when working with data from real-world devices, e. g. controlling a robotic arm, interpolation might not be sufficient. It could happen that future data lies outside of the training domain, e. g. when the arm is temporarily operated outside of its specifications. For the sake of robustness and safety it is desirable in such a case to have a regression model that continues to make good predictions, or at least does not fail catastrophically. This setting, which we call extrapolation generalization, is the topic of the present paper. We are particularly interested in regression tasks for systems that can be described by real-valued analytic expression, e. g. mechanical systems such as a pendulum or a robotic arm. These are typically governed by a highly nonlinear function but it is nevertheless possible, in principle, to infer their behavior on an extrapolation domain from their behavior elsewhere. We make two main contributions: 1) a new type of network that can learn analytical expressions and is able to extrapolate to unseen domains and 2) a model selection strategy tailored to the extrapolation setting. The following section describes the setting of regression and extrapolation. Afterwards we introduce our method and discuss the architecture, its training, and its relation to prior art. We present our results in the Section Experimental evaluation and close with conclusions. REGRESSION AND EXTRAPOLATION We consider a multivariate regression problem with a training set {(x1, y1), . . . , (xN , yN )} with x ∈ R, y ∈ R. Because our main interest lies on extrapolation in the context of learning the dynamics of physical systems we assume the data originates from an unknown analytical function (or system of functions), φ : R → R with additive zero-mean noise, ξ, i. e. y = φ(x) + ξ and Eξ = 0. The function φ may, for instance, reflect a system of ordinary differential equations that govern the movements of a robot arm or the like. The general task is to learn a function ψ : R → R that approximates the true functional relation as well as possible in the squared loss sense, i. e. achieves minimal expected error E‖ψ(x) − φ(x)‖2. In practice, we only have particular examples of the function values available and measure the quality of predicting in terms of the empirical error on

Ex Output:
EXTRAPOLATION AND LEARNING EQUATIONS


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There is an increasing consensus among researchers that making a computer emotionally intelligent with the ability to decode human affective states would allow a more meaningful and natural way of human-computer interactions (HCIs). One unobtrusive and non-invasive way of recognizing human affective states entails the exploration of how physiological signals vary under different emotional experiences. In particular, this paper explores the correlation between autonomically-mediated changes in multimodal body signals and discrete emotional states. In order to fully exploit the information in each modality, we have provided an innovative classification approach for three specific physiological signals including Electromyogram (EMG), Blood Volume Pressure (BVP) and Galvanic Skin Response (GSR). These signals are analyzed as inputs to an emotion recognition paradigm based on fusion of a series of weak learners. Our proposed classification approach showed 88.1% recognition accuracy, which outperformed the conventional Support Vector Machine (SVM) classifier with 17% accuracy improvement. Furthermore, in order to avoid information redundancy and the resultant over-fitting, a feature reduction method is proposed based on a correlation analysis to optimize the number of features required for training and validating each weak learner. Results showed that despite the feature space dimensionality reduction from 27 to 18 features, our methodology preserved the recognition accuracy of about 85.0%. This reduction in complexity will get us one step closer towards embedding this human emotion encoder in the wireless and wearable HCI platforms.

Ex Output:
Decoding Emotional Experience through Physiological Signal Processing


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This paper considers the problem of learning, from samples, the depen-<lb>dency structure of a system of linear stochastic differential equations,<lb>when some of the variables are latent. In particular, we observe the time<lb>evolution of some variables, and never observe other variables; from this,<lb>we would like to find the dependency structure between the observed vari-<lb>ables – separating out the spurious interactions caused by the (marginal-<lb>izing out of the) latent variables’ time series. We develop a new method,<lb>based on convex optimization, to do so in the case when the number of<lb>latent variables is smaller than the number of observed ones. For the case<lb>when the dependency structure between the observed variables is sparse,<lb>we theoretically establish a high-dimensional scaling result for structure re-<lb>covery. We verify our theoretical result with both synthetic and real data<lb>(from the stock market).

Ex Output:

Learning with Latent Factors in Time Series