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Monotonically Decreasing Sequence of Divergences
Tomohiro Nishiyama
Divergences are quantities that measure discrepancy between two probability distributions and play an important role in various fields such as statistics and machine learning. Dive…
A New Lower Bound for Kullback-Leibler Divergence Based on Hammersley-Chapman-Robbins Bound
Tomohiro Nishiyama
In this paper, we derive a useful lower bound for the Kullback-Leibler divergence (KL-divergence) based on the Hammersley-Chapman-Robbins bound (HCRB). The HCRB states that the var…
Cramér-Rao-type Bound and Stam's Inequality for Discrete Random Variables
Tomohiro Nishiyama
The variance and the entropy power of a continuous random variable are bounded from below by the reciprocal of its Fisher information through the Cramér-Rao bound and the Stam's in…
Inequalities between -norms for log-concave distributions
Tomohiro Nishiyama
Log-concave distributions include some important distributions such as normal distribution, exponential distribution and so on. In this note, we show inequalities between two Lp-no…
-norm inequality using q-moment and its applications
Tomohiro Nishiyama
For a measurable function on a set which has a finite measure, an inequality holds between two Lp-norms. In this paper, we show similar inequalities for the Euclidean space and the…