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Register a new userTwin Neural Network Regression is a Semi-Supervised Regression Algorithm
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Added by
Sebastian Johann Wetzel
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Twin neural network regression (TNNR) is a semi-supervised regression algorithm, it can be trained on unlabelled data points as long as other, labelled anchor data points, are present. TNNR is trained to predict differences between the target values of two different data points rather than the targets themselves. By ensembling predicted differences between the targets of an unseen data point and all training data points, it is possible to obtain a very accurate prediction for the original regression problem. Since any loop of predicted differences should sum to zero, loops can be supplied to the training data, even if the data points themselves within loops are unlabelled. Semi-supervised training improves TNNR performance, which is already state of the art, significantly.
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Labelled data often comes at a high cost as it may require recruiting human labelers or running costly experiments. At the same time, in many practical scenarios, one already has access to a partially labelled, potentially biased dataset that can help with the learning task at hand. Motivated by such settings, we formally initiate a study of $semi-supervised$ $active$ $learning$ through the frame of linear regression. In this setting, the learner has access to a dataset $X in mathbb{R}^{(n_1+n_2) times d}$ which is composed of $n_1$ unlabelled examples that an algorithm can actively query, and $n_2$ examples labelled a-priori. Concretely, denoting the true labels by $Y in mathbb{R}^{n_1 + n_2}$, the learners objective is to find $widehat{beta} in mathbb{R}^d$ such that, begin{equation} | X widehat{beta} - Y |_2^2 le (1 + epsilon) min_{beta in mathbb{R}^d} | X beta - Y |_2^2 end{equation} while making as few additional label queries as possible. In order to bound the label queries, we introduce an instance dependent parameter called the reduced rank, denoted by $R_X$, and propose an efficient algorithm with query complexity $O(R_X/epsilon)$. This result directly implies improved upper bounds for two important special cases: (i) active ridge regression, and (ii) active kernel ridge regression, where the reduced-rank equates to the statistical dimension, $sd_lambda$ and effective dimension, $d_lambda$ of the problem respectively, where $lambda ge 0$ denotes the regularization parameter. For active ridge regression we also prove a matching lower bound of $O(sd_lambda / epsilon)$ on the query complexity of any algorithm. This subsumes prior work that only considered the unregularized case, i.e., $lambda = 0$.
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We propose a novel semi-supervised structured output prediction method based on local linear regression in this paper. The existing semi-supervise structured output prediction methods learn a global predictor for all the data points in a data set, which ignores the differences of local distributions of the data set, and the effects to the structured output prediction. To solve this problem, we propose to learn the missing structured outputs and local predictors for neighborhoods of different data points jointly. Using the local linear regression strategy, in the neighborhood of each data point, we propose to learn a local linear predictor by minimizing both the complexity of the predictor and the upper bound of the structured prediction loss. The minimization problem is solved by sub-gradient descent algorithms. We conduct experiments over two benchmark data sets, and the results show the advantages of the proposed method.
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