Comparing representational geometries using whitened unbiased-distance-matrix similarity
Comparing representational geometries using whitened unbiased-distance-matrix similarity
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DOI：
10.51628/001c.27664
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发表时间：
2020-07
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通讯作者：
J. Diedrichsen;Eva Berlot;Marieke Mur;Heiko H. Schütt;Mahdiyar Shahbazi;N. Kriegeskorte
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文献类型：
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作者：
J. Diedrichsen;Eva Berlot;Marieke Mur;Heiko H. Schütt;Mahdiyar Shahbazi;N. Kriegeskorte
表征相似性分析（RSA）通过研究神经活动模式如何反映实验条件来测试大脑计算模型。模型不是直接预测活动模式，而是预测表征的几何形状，如表征相异性矩阵（RDM）所定义的，该矩阵捕获实验条件在多大程度上与相似或不相似的活动模式相关联。因此，RSA首先通过计算每对条件的相异性度量来量化代表性几何，然后将估计的代表性相异性与每个模型预测的相异性进行比较。在这里，我们解决RSA的两个核心挑战：首先，相异性度量，如欧几里得，马氏和相关距离，是有偏见的测量噪声，这可能会导致不正确的推断。无偏相异度估计可以通过交叉验证获得，代价是方差增加。其次，成对相异性估计值在统计上并不独立，忽略这种依赖性会使模型比较在统计上次优。我们提出了一个有偏和无偏估计的平方欧几里德和马氏距离的均值和（协）方差的分析表达式，使我们能够量化的偏差方差权衡。我们还利用相异度估计的协方差的解析表达式来消除RDM估计的误差。这导致了一个新的RDM相似性标准，白化无偏RDM余弦相似性（WUC），它允许接近最佳的模型选择与相关测量噪声的鲁棒性相结合。
Representational similarity analysis (RSA) tests models of brain computation by investigating how neural activity patterns reflect experimental conditions. Instead of predicting activity patterns directly, the models predict the geometry of the representation, as defined by the representational dissimilarity matrix (RDM), which captures to what extent experimental conditions are associated with similar or dissimilar activity patterns. RSA therefore first quantifies the representational geometry by calculating a dissimilarity measure for each pair of conditions, and then compares the estimated representational dissimilarities to those predicted by each model. Here we address two central challenges of RSA: First, dissimilarity measures such as the Euclidean, Mahalanobis, and correlation distance, are biased by measurement noise, which can lead to incorrect inferences. Unbiased dissimilarity estimates can be obtained by crossvalidation, at the price of increased variance. Second, the pairwise dissimilarity estimates are not statistically independent, and ignoring this dependency makes model comparison statistically suboptimal. We present an analytical expression for the mean and (co)variance of both biased and unbiased estimators of the squared Euclidean and Mahalanobis distance, allowing us to quantify the bias-variance trade-off. We also use the analytical expression of the covariance of the dissimilarity estimates to whiten the RDM estimation errors. This results in a new criterion for RDM similarity, the whitened unbiased RDM cosine similarity (WUC), which allows for near-optimal model selection combined with robustness to correlated measurement noise.