The ratio p/(1 − p) is called the odds of the event y given x, and log[p/(1 − p)]
is called the log odds. Since probabilities range between 0 and 1, odds range
between 0 and +∞ and log odds range unboundedly between −∞ and +∞. A
linear expression of the form α +
P
j
β
j
x
j
can also take unbounded values, so
it is reasonable to use a linear expression as a model for log odds, but not as a
model for odds or for probabilities. Essentially, logistic regression is the simplest
possible model for a random yes/no outcome that depends linearly on predictors
x
1
to x
d
.
For each feature j, exp(β
j
x
j
) is a multiplicative scaling factor on the odds
p/(1 − p). If the predictor x
j
is binary, then exp(β
j
) is the extra odds of having
the outcome y = 1 when x
j
= 1, compared to when x
j
= 0.
Note that it is acceptable, and indeed often beneficial, to include a large num-
ber of features in a logistic regression model. Some features may be derived,
i.e. computed as deterministic functions of other features. One great advantage
of logistic regression in comparison to other classifiers is that the training process
will find optimal coefficients for features regardless of whether the features are
correlated. Other learning methods, in particular naive Bayes, do not work well
when the feature values of training or test examples are correlated.
A second major advantage of logistic regression is that it gives well-calibrated
probabilities. The numerical values p(y = 1|x) given by a logistic regression
model are not just scores where a larger score means that the example x is more
likely to have label y = 1; they are meaningful conditional probabilities. This
implies that given a set of n test examples with numerical predictions v
1
to v
n
,
the number of examples in the set that are truly positive will be close to
P
n
i=1
v
i
,
whatever this sum is.
Last but not least, a third major advantage of logistic regression is that it is not
sensitive to unbalanced training data. What this means is that even if one class (ei-
ther the positive or negative examples) is much larger than the other (correspond-
ingly, the negative or positive examples), logistic regression training encounters
no difficulties and the final classifier will still be well-calibrated. The conditional
probabilities predicted by the trained classifier will range below and above the
base rate, i.e. the unconditional probability p(y = 1).
5
剩余26页未读，继续阅读
GladyoUcaMe
- 粉丝: 47
- 资源: 4
我的内容管理
展开
最新资源
- 新型矿用本安直流稳压电源设计：双重保护电路
- 煤矿掘进工作面安全因素研究：结构方程模型
- 利用同位素位移探测原子内部新型力
- 钻锚机钻臂动力学仿真分析与优化
- 钻孔成像技术在巷道松动圈检测与支护设计中的应用
- 极化与非极化ep碰撞中J/ψ的Sivers与cos2φ效应：理论分析与COMPASS验证
- 新疆矿区1200m深孔钻探关键技术与实践
- 建筑行业事故预防：综合动态事故致因理论的应用
- 北斗卫星监测系统在电网塔形实时监控中的应用
- 煤层气羽状水平井数值模拟：交替隐式算法的应用
- 开放字符串T对偶与双空间坐标变换
- 煤矿瓦斯抽采半径测定新方法——瓦斯储量法
- 大倾角大采高工作面设备稳定与安全控制关键技术
- 超标违规背景下的热波动影响分析
- 中国煤矿选煤设计进展与挑战：历史、现状与未来发展
- 反演技术与RBF神经网络在移动机器人控制中的应用
资源上传下载、课程学习等过程中有任何疑问或建议，欢迎提出宝贵意见哦~我们会及时处理！
点击此处反馈
