Typically, one approaches a supervised machine learning problem by writing down an objective function and finding a hypothesis that minimizes it. This is equivalent to finding the Maximum A Posteriori (MAP) hypothesis for a Boltzmann distribution. However, MAP is not a robust statistic. We present an alternative approach by defining a median of the distribution, which we show is both more robust, and has good generalization guarantees. We present algorithms to approximate this median.<\/p>\n\n\n\n
One contribution of this work is an efficient method for approximating the Tukey median. The Tukey median, which is often used for data visualization and outlier detection, is a special case of the family of medians we define: however, computing it exactly is exponentially slow in the dimension. Our algorithm approximates such medians in polynomial time while making weaker assumptions than those required by previous work.<\/p>\n","protected":false},"excerpt":{"rendered":"
Typically, one approaches a supervised machine learning problem by writing down an objective function and finding a hypothesis that minimizes it. This is equivalent to finding the Maximum A Posteriori (MAP) hypothesis for a Boltzmann distribution. However, MAP is not a robust statistic. 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