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carefree-ml implemented Machine Learning algorithms with numpy, mainly for educational use


carefree-ml requires Python 3.8 or higher.

pip install carefree-ml


git clone
cd carefree-ml
pip install -e .

Basic Usage

See tests/usages/ for more example

from cfml import *
from cfdata.tabular import TabularDataset

# fetch dataset
boston =
# make a model
lr = Base.make("linear_regression")
# fit the model*boston.xy)
# plot loss curve
# make predictions
predictions = lr.predict(boston.x)

...or use methods chaining

import os
from cfml import *
from cfdata.tabular import *

# fetch dataset
prices_file = os.path.join("tests", "datasets", "prices.txt")
prices = TabularData(task_type=TaskTypes.REGRESSION).read(prices_file).to_dataset()
# one liner

Supported Algorithms

  • 1-dimensional polynomial fit (np.polyfit)
  • Linear Models (Linear Regression, Logistic Regression, Linear SVC, Linear SVR)
  • Naive Bayes (Multinomial NB, Gaussian NB)
  • Support Vector Machine (SVC, SVR)
  • Fully Connected Neural Network (FCNN-clf, FCNN-reg)


It's up to you! Issues are welcomed :)

Q & A

  • I used Google Translate to help me translate Chinese to English

Why carefree-ml?


Why shall we choose to use (or learn from) carefree-ml?

carefree-ml 其实源于我一直以来未竟的两个心愿

  • 探索机器学习算法到底可以简化成什么样
  • 探索各种机器学习算法间的共性究竟有多少

carefree-ml actually stems from my two unfinished wishes

  • Explore how machine learning algorithms can be simplified
  • Explore commonality among various machine learning algorithms

如果你恰好有这个疑惑,又或是想教导其他人这方面的直观,那么 carefree-ml 可能就会比较适合你。但是,如果你对机器学习有着更高的追求,对各种美妙的性质有着探索的欲望,那么 carefree-ml 反而可能会激怒你,因为它省略了很多前人研究出来的结晶

If you happen to have these doubts, or willing to teach others about some intuitions, then carefree-ml may be suitable for you. However, if you have a higher pursuit of machine learning and desire to explore more wonderful properties from machine learning, then carefree-ml may irritate you, because it omits many of them


First of all, we know that machine learning (and deep learning) algorithms can often be transformed into unconstrained optimization problems. If some special properties (sparseness, convergence speed, etc.) are not considered, the gradient descent based methods can be the most widely use

因此,carefree-ml 实现的第一大模块,就是一套简单的梯度下降的优化框架,旨在用较少的代码去 handle 大部分情况;在实现一个机器学习算法时,也会优先考虑采用梯度下降算法去实现(这其实就是 carefree-ml 所做的最大的简化了,下面的例子就说明了这一点)

Therefore, the first major module implemented by carefree-ml is a simple gradient descent optimization framework, which is designed to handle most cases with less code. After that, when implementing a machine learning algorithm in carefree-ml, gradient descent based methods will also be considered first (this is actually the biggest simplification done by carefree-ml, the following example of LinearRegression illustrates this)

那么,在这种思想下,我们是如何实现 LinearRegressionLogisticRegression 的呢?首先我们可能都知道:

  • 两者都是 线性模型
  • 前者做的是 回归 问题,后者做的是 分类 问题
  • 后者在输出时使用了 sigmoid 激活函数

So, under this idea, how do we implement LinearRegression and LogisticRegression? First of all we may all know that:

  • Both of them are Linear Models
  • The former deals with regression problems, while the latter deals with classification problems
  • The latter used sigmoid function to output the probability predictions


  • 如果前者使用 mse 作为损失函数,后者使用 cross_entropy 作为损失函数,那么它们参数的梯度将会几乎是一模一样的(只差一个倍数)

But there's one thing that we might not have noticed before:

  • If we use mse loss in LinearRegression and use cross_entropy loss in LogisticRegression, then thier parameters' gradients will be almost identical (except for a multiple factor)

那么,既然它们如此相似,差异点仅在于几个小部分,它们的实现也应该很像才对。所以,在 carefree-ml 中,它们的实现的主体将分别是:

Since they are so similar and the differences are only in a few small parts, their implementation should be very similar as well. Therefore, in carefree-ml, the main part of their implementations will be as follows:

class LinearRegression(LinearRegressorMixin, RegressorBase):
    def __init__(self):
        self._w = self._b = None
class LogisticRegression(LinearBinaryClassifierMixin, ClassifierBase):
    def __init__(self):
        self._w = self._b = None
        self._sigmoid = Activations("sigmoid")

    def _predict_normalized(self, x_normalized):
        affine = super()._predict_normalized(x_normalized)
        return self._sigmoid(affine)

这里的设计,其实就体现了 carefree-ml 想将机器学习算法“简化”的思想。因为我们知道,mse loss 下的 LinearRegression 是有显式解的(因为就是一个最小二乘法),但是我们仍然用梯度下降去求解它,因为这样它将会与 LogisticRegression 共享大部分代码

The design here actually embodies the idea that carefree-ml wants to simplify machine learning algorithms. Because we know that LinearRegression under mse loss has an explicit solution (because it's simply a Least Squares problem), but we still use gradient descent to solve it because in this case it will share most of its code with LogisticRegression's code

当然,这种简化(将许多算法都归结为无约束优化问题并用梯度下降法求解)并不是全是坏处,比如我们完全可以在代码几乎不变的前提下,去求解 l1 loss、或者其它形形色色的 loss 下的 LinearRegression

Of course, this simplification (reducing many algorithms to unconstrained optimization problems and solving them by gradient descent) has its advantage too. For example, we can solve l1 loss or other losses in LinearRegression under the premise that the corresponding training codes will be almost unchanged

再比如说 svm。虽然支持向量分类和支持向量回归看上去是非常不一样的两种算法,但是抽丝剥茧之后,如果用梯度下降法去求解,就会发现其实大部分代码仍然是共享的,这也恰好辅证了为何它们同属 svm 的范畴:

Another example is svm. Although support vector classification and support vector regression seem to be very different algorithms, but after pulling the cocoon, if you use gradient descent based methods to solve them, you will find that most of the codes are still shared. This also justifies why they belong to the same category - svm:

class CoreSVCMixin:
    def _preprocess_data(x, y):
        y_svm = y.copy()
        y_svm[y_svm == 0] = -1
        return x, y_svm

    def get_diffs(y_batch, predictions):
        return {"diff": 1. - y_batch * predictions, "delta_coeff": -y_batch}

class SVCMixin(BinaryClassifierMixin, SVMMixin, metaclass=ABCMeta):
    def predict_prob(self, x):
        affine = self.predict_raw(x)
        sigmoid = Activations.sigmoid(np.clip(affine, -2., 2.) * 5.)
        return np.hstack([1. - sigmoid, sigmoid])
class CoreSVRMixin:
    def get_diffs(self, y_batch, predictions):
        raw_diff = predictions - y_batch
        l1_diff = np.abs(raw_diff)
        if self.eps <= 0.:
            tube_diff = l1_diff
            tube_diff = l1_diff - self.eps
        return {"diff": tube_diff, "delta_coeff": np.sign(raw_diff)}

class SVRMixin(SVMMixin, metaclass=ABCMeta):
    def predict(self, x):
        return self.predict_raw(x)

然后真正实现 svm 算法时,就只需继承不同的类即可:

After these, when you actually implement the svm algorithms, you only need to inherit different classes:

class SVC(CoreSVCMixin, SVCMixin, ClassifierBase):
    def __init__(self,
                 kernel: str = "rbf"):
        self._kernel = Kernel(kernel)
class SVR(CoreSVRMixin, SVRMixin, RegressorBase):
    def __init__(self,
                 eps: float = 0.,
                 kernel: str = "rbf"):
        self._eps = eps
        self._kernel = Kernel(kernel)


Of course, the real core codes (SVMMixin) still have to be written

此外,除了相似算法间的代码共享,carefree-ml 还致力于常见工程功能上的代码共享。比如说,我们一般可能需要:

  • 对输入的特征进行规范化处理(normalization)
  • 在回归问题中对标签进行 normalization
  • 在二分类问题中通过 roc curve 以及具体的 metric 来挑选出最优分类阈值

In addition, besides code sharing between similar algorithms, carefree-ml is also dedicated to sharing codes on common engineering functions. For example, we may generally need:

  • Normalize the input features
  • Normalize the labels in regression problems
  • Utilize roc curve to find the best threshold of specific metric in binary classification problems

这些工程上的东西,也是理应进行代码共享的。因此,carefree-ml 确实在 cfml.models.mixins 中,实现了 NormalizeMixinBinaryClassifierMixin,用于实现这些可能被广泛运用的功能

These engineering functions are also supposed to share codes. Therefore, carefree-ml implements NormalizeMixin and BinaryClassifierMixin in cfml.models.mixins for these functions that may be widely used

What can carefree-ml do?

carefree-ml 能做到什么?

What can carefree-ml do?

首先,最近其实有很多用 numpy 实现海量算法的 repo,所以单单用 numpy 来作为卖点是不合适的。我个人认为的话,carefree-ml 之所以还算有些特色,主要是由于如下三点:

  • 实现了一个轻量级的、泛用性比较好的梯度下降框架
  • 比起模型的性能,更注重于让算法间共享逻辑、代码;正因此,总代码量会比较少
  • 即使在第二点的“桎梏”下,在小的、比较简单的数据集上,无论是速度还是性能,都是可以锤掉 scikit-learn 的友商产品的

First of all, there are actually a lot of repos that use numpy to implement massive algorithms recently, so it is not appropriate to use numpy as a selling point. In my personal opinion, the reason why carefree-ml is still special are shown as follows:

  • Implemented a lightweight gradient descent framework which can be used in a wide range of problems
  • Compared with the performance of the model, it focused more on the sharing of logic and codes between algorithms. Therefore, the total amount of code will be less
  • Even under the 'shackles' of the second point, on small and relatively simple datasets, it can beat scikit-learn in either speed or performance to some extend


Here's how you can test it (included installation procedures)

git clone
cd carefree-ml
pip install -e .
cd tests/unittests


Here's some fragments from the outputs:

~~~  [ info ] timing for    cfml_fcnn     : 0.310764
~~~  [ info ] timing for   sklearn_fcnn   : 0.549960
|             cfml_fcnn  |    mae     |  2.682794  |  <-  
|          sklearn_fcnn  |    mae     |  3.969561  |
|             cfml_fcnn  |    mse     |  15.635315  |  <-  
|          sklearn_fcnn  |    mse     |  30.890426  |
~~~  [ info ] timing for     cfml_lr      : 0.039881
~~~  [ info ] timing for    sklearn_lr    : 0.654799
|               cfml_lr  |    auc     |  0.996287  |  <-  
|            sklearn_lr  |    auc     |  0.994675  |
|               cfml_lr  |    acc     |  0.980668  |  <-  
|            sklearn_lr  |    acc     |  0.957821  |
# gaussian naive bayes
~~~  [ info ] timing for     cfml_gnb     : 0.000000
~~~  [ info ] timing for   sklearn_gnb    : 0.001028
# multinomial naive bayes
~~~  [ info ] timing for     cfml_mnb     : 0.003990
~~~  [ info ] timing for   sklearn_mnb    : 0.007011
~~~  [ info ] timing for     cfml_svc     : 0.207024
~~~  [ info ] timing for    cfml_l_svc    : 0.023937
~~~  [ info ] timing for    sklearn_lr    : 0.571722
~~~  [ info ] timing for   sklearn_svc    : 0.007978
~~~  [ info ] timing for  sklearn_l_svc   : 0.148603
|            cfml_l_svc  |    auc     |  0.996300  |
|              cfml_svc  |    auc     |  1.000000  |  <-  
|            sklearn_lr  |    auc     |  0.994675  |
|            cfml_l_svc  |    acc     |  0.985940  |
|              cfml_svc  |    acc     |  1.000000  |  <-  
|         sklearn_l_svc  |    acc     |  0.848858  |
|            sklearn_lr  |    acc     |  0.957821  |
|           sklearn_svc  |    acc     |  0.922671  |
~~~  [ info ] timing for     cfml_svr     : 0.090758
~~~  [ info ] timing for    cfml_l_svr    : 0.027925
~~~  [ info ] timing for   sklearn_svr    : 0.008012
~~~  [ info ] timing for  sklearn_l_svr   : 0.165730
|            cfml_l_svr  |    mae     |  3.107422  |  <-  
|              cfml_svr  |    mae     |  5.106989  |
|         sklearn_l_svr  |    mae     |  4.654314  |
|           sklearn_svr  |    mae     |  5.259882  |
|            cfml_l_svr  |    mse     |  24.503884  |  <-  
|              cfml_svr  |    mse     |  66.583145  |
|         sklearn_l_svr  |    mse     |  39.598211  |
|           sklearn_svr  |    mse     |  66.818898  |

当然了,吹是这么吹,最后我们还是得负责任地说一句:从实用性、泛化性来说,scikit-learn 肯定是吊打 carefree-ml 的(比如 carefree-ml 完全不支持稀疏数据)。但是,正如我一开始所说,carefree-ml 只是想探索“机器学习算法到底可以简化成什么样”的产物,所以在简单的数据集上,拟合能力、拟合速度超过 scikit-learn 其实也并不奇怪

Of course, in the end we still have to say something responsibly: from the perspective of practical use and generalization, scikit-learn will beat carefree-ml by all means (for short, carefree-ml does not support sparse data). However, as I said at the beginning, carefree-ml focus on exploring how machine learning algorithms can be simplified. So it is not surprising that carefree-ml can exceed scikit-learn on small & simple datasets in fitting capacity & fitting speed.


Notice that the above experimental results are the results on the training set, so it can only reflect the fitting capacity, not the generalization capacity

How can I utilize carefree-ml?

我能怎么使用 carefree-ml

How can I utilize carefree-ml?

从实用性角度来看,也许 carefree-ml 实现的那套简易梯度下降框架,是相对而言最实用的。但即便是它,也会被 pytorch 轻松吊锤

From a practical point of view, perhaps the lightweight gradient descent framework implemented by carefree-ml is relatively the most useful tool. But even it will be easily defeated and replaced by pytorch

所以,正如我开头所说,mainly for educational use,可能教育意义会大于实用意义。虽然本人学术能力不咋地,但是毕竟该 repo 的初衷应该很少搞学术的会看得起并加以研究,所以从这个角度来看,carefree-ml 也许能给你带来一些新的体会

So, as I said at the beginning, carefree-ml is mainly for educational use, so the meaning of education may be greater than the practical meaning. Although my academic ability is not good at all, the original intention of this repo might not be worthy of academic researching. So from this perspective, carefree-ml may give you some new sights


carefree-ml is MIT licensed, as found in the LICENSE file.


carefree-ml implemented Machine Learning algorithms with numpy, mainly for educational use








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