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/*
* BotSharp.Algorithm
* Copyright (C) 2018 Haiping Chen
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
using BotSharp.Algorithm.Statistics;
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
namespace BotSharp.Algorithm.Estimators
{
/// <summary>
/// Lidstone smoothing is a technique used to smooth categorical data.
/// In statistics, it's called additive smoothing or Laplace smoothing.
/// Given an observation x = (x1, …, xd) from a multinomial distribution with N trials, a "smoothed" version of the data gives the estimator.
/// https://en.wikipedia.org/wiki/Additive_smoothing
/// Used as Multinomial Naive Bayes
/// </summary>
public class AdditiveSmoothing : IEstimator
{
/// <summary>
/// 1 > α > 0 is the smoothing parameter is Lidstone
/// α = 1 is Laplace
/// α = 0 no smoothing
/// </summary>
public double Alpha { get; set; }
/// <summary>
/// Probability
/// </summary>
/// <param name="dist">distribution</param>
/// <param name="sample">sample value</param>
/// <returns></returns>
public double Prob(List<Probability> dist, string sample)
{
if(Alpha == 0)
{
Alpha = 0.5D;
}
// observation x = (x1, ..., xd)
var p = dist.Find(f => f.Value == sample);
int x = p == null ? 0 : p.Freq;
// N trials
int _N = dist.Sum(f => f.Freq);
int _d = dist.Count;
return (x + Alpha) / (_N + Alpha * _d);
}
public double Prob(List<Tuple<string, double>> dist, string sample)
{
if (Alpha == 0)
{
Alpha = 0.5D;
}
// observation x = (x1, ..., xd)
var p = dist.Find(f => f.Item1 == sample);
double x = p == null ? 0D : p.Item2;
// N trials
double _N = dist.Sum(f => f.Item2);
int _d = dist.Count;
return (x + Alpha) / (_N + Alpha * _d);
}
}
}