An information estimation apparatus configured to perform an estimation process of input data of mobile objects, the input data being images, and to output an estimation result for the mobile objects and a combined variance representing a confidence interval for the estimation result, the estimation result being a classification as any of "pedestrian", "car" and "bicycle", using a neural network including an integrated layer that combines a dropout layer for dropping out a part of the input data and a fully connected layer for computing a weight, and an output layer, the information estimation apparatus comprising: a data analysis unit configured to determine, based on a numerical distribution of terms formed by respective products of each vector element of the input data to the integrated layer having a multivariate distribution and the weight, a data type of each vector element of output data from the integrated layer having a multivariate distribution; an estimated confidence interval computation unit configured to apply a method comprising an approximation computation associated with the data type determined by the data analysis unit to a computation in the integrated layer, to analytically compute a variance of each vector element of the output data from the integrated layer based on the input data to the integrated layer, wherein the data analysis unit is further configured to determine the data type, based on a result of determining whether or not the terms formed by the respective products of each vector element of the input data to the integrated layer and the weight include a peak term that is exceptionally larger than other terms, and a computation processing unit configured to process the input data and output the estimation result, wherein, in the output layer of the neural network, the combined variance representing the confidence interval is computed, wherein the estimation result is output by the output layer of the neural network. a data analysis unit configured to determine, based on a numerical distribution of terms formed by respective products of each vector element of the input data to the integrated layer having a multivariate distribution and the weight, a data type of each vector element of output data from the integrated layer having a multivariate distribution; an estimated confidence interval computation unit configured to apply a method comprising an approximation computation associated with the data type determined by the data analysis unit to a computation in the integrated layer, to analytically compute a variance of each vector element of the output data from the integrated layer based on the input data to the integrated layer, wherein the data analysis unit is further configured to determine the data type, based on a result of determining whether or not the terms formed by the respective products of each vector element of the input data to the integrated layer and the weight include a peak term that is exceptionally larger than other terms, and a computation processing unit configured to process the input data and output the estimation result, wherein, in the output layer of the neural network, the combined variance representing the confidence interval is computed, wherein the estimation result is output by the output layer of the neural network.