In many domains such as medicine, training data is in short supply. In such cases, external knowledge is often helpful in building predictive models. We propose a novel method to incorporate publicly available domain expertise to build accurate models. Specifically, we use word2vec models trained on a domain-specific corpus to estimate the relevance of each feature's text description to the prediction problem. We use these relevance estimates to rescale the features, causing more important features to experience weaker regularization. We apply our method to predict the onset of five chronic diseases in the next five years in two genders and two age groups. Our rescaling approach improves the accuracy of the model, particularly when there are few positive examples. Furthermore, our method selects 60 fewer features, easing interpretation by physicians. Our method is applicable to other domains where feature and outcome descriptions are available.
Our work diverges from prior work because our target task'' uses structured medical data, but we transfer knowledge from unstructured external sources to understand the relationship between the of the features and the outcome. For each feature, we estimate its relevance to predicting the outcome, and use these relevance estimates to rescale the feature matrix. This rescaling procedure is equivalent to the feature selection methods, adaptive lasso ( @cite_9 ) and nonnegative garotte ( @cite_16 ). In the adaptive lasso, the adaptive scaling factors are usually obtained from the ordinary least squares estimate. By contrast, we inferred these scaling factors from an expert text corpus. This technique leverages auxiliary data and can thus be applied when the original training data are not sufficient to obtain reliable least squares estimates. Other approaches to feature selection for predicting disease onset include augmenting expert-derived risk factors with data-driven variables ( @cite_11 ) and performing regression in multiple dimensions simultaneously ( @cite_17 ).
@cite_9 @cite_16 @cite_17 @cite_11
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In the sparse linear regression setting, we consider testing the significance of the predictor variable that enters the current lasso model, in the sequence of models visited along the lasso solution path. We propose a simple test statistic based on lasso fitted values, called the covariance test statistic, and show that when the true model is linear, this statistic has an Exp(1) asymptotic distribution under the null hypothesis (the null being that all truly active variables are contained in the current lasso model). Our proof of this result for the special case of the first predictor to enter the model (i.e., testing for a single significant predictor variable against the global null) requires only weak assumptions on the predictor matrix X. On the other hand, our proof for a general step in the lasso path places further technical assumptions on X and the generative model, but still allows for the important high-dimensional case p > n, and does not necessarily require that the current lasso model achieves perfect recovery of the truly active variables. Of course, for testing the significance of an additional variable between two nested linear models, one typically uses the chi-squared test, comparing the drop in residual sum of squares (RSS) to a χ12 distribution. But when this additional variable is not fixed, and has been chosen adaptively or greedily, this test is no longer appropriate: adaptivity makes the drop in RSS stochastically much larger than χ12 under the null hypothesis. Our analysis explicitly accounts for adaptivity, as it must, since the lasso builds an adaptive sequence of linear models as the tuning parameter λ decreases. In this analysis, shrinkage plays a key role: though additional variables are chosen adaptively, the coefficients of lasso active variables are shrunken due to the l1 penalty. Therefore, the test statistic (which is based on lasso fitted values) is in a sense balanced by these two opposing properties—adaptivity and shrinkage—and its null distribution is tractable and asymptotically Exp(1). Despite superior training outcomes, adaptive optimization methods such as Adam, Adagrad or RMSprop have been found to generalize poorly compared to Stochastic gradient descent (SGD). These methods tend to perform well in the initial portion of training but are outperformed by SGD at later stages of training. We investigate a hybrid strategy that begins training with an adaptive method and switches to SGD when appropriate. Concretely, we propose SWATS, a simple strategy which switches from Adam to SGD when a triggering condition is satisfied. The condition we propose relates to the projection of Adam steps on the gradient subspace. By design, the monitoring process for this condition adds very little overhead and does not increase the number of hyperparameters in the optimizer. We report experiments on several standard benchmarks such as: ResNet, SENet, DenseNet and PyramidNet for the CIFAR-10 and CIFAR-100 data sets, ResNet on the tiny-ImageNet data set and language modeling with recurrent networks on the PTB and WT2 data sets. The results show that our strategy is capable of closing the generalization gap between SGD and Adam on a majority of the tasks. Using the l1-norm to regularize the least-squares criterion, the batch least-absolute shrinkage and selection operator (Lasso) has well-documented merits for estimating sparse signals of interest emerging in various applications where observations adhere to parsimonious linear regression models. To cope with high complexity, increasing memory requirements, and lack of tracking capability that batch Lasso estimators face when processing observations sequentially, the present paper develops a novel time-weighted Lasso (TWL) approach. Performance analysis reveals that TWL cannot estimate consistently the desired signal support without compromising rate of convergence. This motivates the development of a time- and norm-weighted Lasso (TNWL) scheme with l1-norm weights obtained from the recursive least-squares (RLS) algorithm. The resultant algorithm consistently estimates the support of sparse signals without reducing the convergence rate. To cope with sparsity-aware recursive real-time processing, novel adaptive algorithms are also developed to enable online coordinate descent solvers of TWL and TNWL that provably converge to the true sparse signal in the time-invariant case. Simulated tests compare competing alternatives and corroborate the performance of the novel algorithms in estimating time-invariant signals, and tracking time-varying signals under sparsity constraints. Recommender problems with large and dynamic item pools are ubiquitous in web applications like content optimization, online advertising and web search. Despite the availability of rich item meta-data, excess heterogeneity at the item level often requires inclusion of item-specific "factors" (or weights) in the model. However, since estimating item factors is computationally intensive, it poses a challenge for time-sensitive recommender problems where it is important to rapidly learn factors for new items (e.g., news articles, event updates, tweets) in an online fashion. In this paper, we propose a novel method called FOBFM (Fast Online Bilinear Factor Model) to learn item-specific factors quickly through online regression. The online regression for each item can be performed independently and hence the procedure is fast, scalable and easily parallelizable. However, the convergence of these independent regressions can be slow due to high dimensionality. The central idea of our approach is to use a large amount of historical data to initialize the online models based on offline features and learn linear projections that can effectively reduce the dimensionality. We estimate the rank of our linear projections by taking recourse to online model selection based on optimizing predictive likelihood. Through extensive experiments, we show that our method significantly and uniformly outperforms other competitive methods and obtains relative lifts that are in the range of 10-15 in terms of predictive log-likelihood, 200-300 for a rank correlation metric on a proprietary My Yahoo! dataset; it obtains 9 reduction in root mean squared error over the previously best method on a benchmark MovieLens dataset using a time-based train test data split.