In this work, we show how inverse regression in the abundant feature setting, together with an interesting statistical construction called sufficient reduction, yields highly flexible models that are a natural fit for model estimation tasks and computer vision. Specifically, we obtain formulations that provide the relevance of individual covariates in the prediction, at the level of specific image examples. This can provide valuable insight into why particular predictions were made. In this motivating example, we extract abundant features across the image to predict the temperature of the scene. Intuitively, if we can compute a meaningful distance between the test image and each training example, we can use the temperature in the nearest training examples to predict the temperature in the test scene. Unfortunately, occlusions and noise can corrupt these distances. If we select all features in the image and weight them uniformly and compute the distance from training example A and the distance from training example B, it's possible that the test image will be closer to B, perhaps due to the snow and B, which resembles parts of the vehicles on the test image. These distances are problematic because the temperature of training example B is much colder than the true temperature of the test scene. Ideally, we want A to be closer to the test image than B. Instead, we compute weights over the test image that reflect the relevance of each feature with respect to the temperature prediction. The weights are specific to each test image. In this example, the vehicles, which occlude the ground, are down weighted. Our weighted distance is a function of the features and weight maps from each instance. The weight maps are multiplied in an element-wise manner. Because the non-vehicle regions of the test image closely resemble the corresponding regions of example A, the test image is closer to A than B according to our weighted distance. Now we will provide a high-level explanation of how our framework obtains the dynamic weights. First, we divide the image into local patches. Each patch makes an independent temperature prediction. In this case, patch 125 highlighted here in yellow, we compute the conditional confidence given the prediction from patch 1, which is assumed to be a sufficient reduction. Similarly, we compute the conditional confidence of patch 125 given the prediction from patch 2 and so on. We compute the weight of patch 125 as the expected conditional confidence over all predictions. This process is repeated for each patch in the image. We see in this example that patches over vehicles, which occlude the ground, are correctly down weighted. Next, we'll look at several interesting examples. In this example, we see that the weights changed dynamically based on the characteristics of each image in the sequence. Notice here that when the trees have leaves, the corresponding patches have higher weight and are therefore more relevant to the temperature prediction. In this example, a hanging declaration occludes the tree behind it. Nearby patches are properly down weighted. Vehicles which frequently change position are also down weighted. VCRHTML document for additional results. Thank you.