Non-parametric Statistical Density Function Synthesizer and Monte Carlo Sampler in CMOS

In this work, we present a CMOS-based sampling circuit to produce random numbers of non-parametric densities for Monte Carlo-based methods. Scaling of purely algorithmic Monte Carlo sampling techniques with problem size is challenging and this severely compromises performance of the application. To overcome this challenge, we present a novel CMOS-based Monte Carlo sampler which can be considered as an “add-on” to the existing random number generator (RNG) circuits to produce non-parametric Monte Carlo samples. Our design employs two statistical techniques, namely: (i) kernel Density estimation (KDE) and (ii) Inverse Sampling. We present a novel CMOS operational transconductance amplifier (OTA) based Sigmoid kernel implementation for non-parametric cumulative density function (CDF) estimation using KDE. Subsequently, we show that inverse sampling can be realized using successive approximation based mixed-signal implementation. OTAs are designed to operate in sub-threshold regime while consuming 300nW. Discussed architecture allows programmability of number of random variable (RV) samples $(N_{Samp})$ and Sigmoid kernel standard deviation $(\sigma_{kernel})$ to ensure reliable CDF estimation. Overall architecture on an average consumes $\sim 750 \mu \mathrm{W}$ while using 50 random samples for CDF estimation at 200 MHz clock frequency.