学习笔记(四）： Representation:Feature Engineering/Qualities of Good Features/Cleaning Data/Feature Sets

目录

Representation

Feature Engineering

Mapping Raw Data to Features

Mapping numeric values

Mapping categorical values

Sparse Representation

Glossay

Qualities of Good Features

Avoid rarely used discrete feature values

Prefer clear and obvious meanings

Don't mix "magic" values with actual data

Account for upstream instability上游不稳定性

Cleaning Data

Scaling feature values

Learn more about scaling

Handling extreme outliers

Binning分档

Learn more about binning boundaries

Scrubbing

Know your data

Additional Information

Glossay

Programming Exercise

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Representation

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A machine learning model can't directly see, hear, or sense input examples. Instead, you must create a representation of the data to provide the model with a useful vantage point into the data's key qualities. That is, in order to train a model, you must choose the set of features that best represent the data.

Learning Objectives

• Map fields from logs and protocol buffers into useful ML features.
• Determine which qualities comprise great features.
• Handle outlier features.
• Investigate the statistical properties of a data set.
• Train and evaluate a model with tf.estimator.

Feature Engineering

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In traditional programming, the focus is on code. In machine learning projects, the focus shifts to representation.

That is, one way developers hone a model is by adding and improving its features.

Mapping Raw Data to Features

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The left side of Figure 1 illustrates raw data from an input data source; the right side illustrates a feature vector, which is the set of floating-point values comprising the examples in your data set.

Feature engineering means transforming raw data into a feature vector. Expect to spend significant time doing feature engineering.

Many machine learning models must represent the features as real-numbered vectors since the feature values must be multiplied by the model weights.

Figure 1. Feature engineering maps raw data to ML features.

Mapping numeric values

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Integer and floating-point data don't need a special encoding because they can be multiplied by a numeric weight. As suggested in Figure 2, converting the raw integer value 6 to the feature value 6.0 is trivial:

Figure 2. Mapping integer values to floating-point values.

Mapping categorical values

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Categorical features have a discrete set of possible values. For example, there might be a feature called street_name with options that include:

{'Charleston Road', 'North Shoreline Boulevard', 'Shorebird Way', 'Rengstorff Avenue'}

Since models cannot multiply strings by the learned weights, we use feature engineering to convert strings to numeric values.

We can accomplish this by defining a mapping from the feature values, which we'll refer to as the vocabulary of possible values, to integers.

Since not every street in the world will appear in our dataset, we can group all other streets into a catch-all "other" category, known as an OOV (out-of-vocabulary) bucket.

Using this approach, here's how we can map our street names to numbers:

• map Charleston Road to 0
• map North Shoreline Boulevard to 1
• map Shorebird Way to 2
• map Rengstorff Avenue to 3
• map everything else (OOV) to 4

However, if we incorporate these index numbers directly into our model, it will impose some constraints that might be problematic:

• We'll be learning a single weight that applies to all streets. For example, if we learn a weight of 6 for street_name, then we will multiply it by 0 for Charleston Road, by 1 for North Shoreline Boulevard, 2 for Shorebird Way and so on. Consider a model that predicts house prices using street_name as a feature. It is unlikely that there is a linear adjustment of price based on the street name, and furthermore this would assume you have ordered the streets based on their average house price. Our model needs the flexibility of learning different weights for each street that will be added to the price estimated using the other features.

• We aren't accounting for cases where street_name may take multiple values. For example, many houses are located at the corner of two streets, and there's no way to encode that information in the street_name value if it contains a single index.

To remove both these constraints, we can instead create a binary vector for each categorical feature in our model that represents values as follows:

• For values that apply to the example, set corresponding vector elements to 1.
• Set all other elements to 0.

The length of this vector is equal to the number of elements in the vocabulary. This representation is called a one-hot encoding when a single value is 1, and a multi-hot encoding when multiple values are 1.

Figure 3 illustrates a one-hot encoding of a particular street: Shorebird Way.

The element in the binary vector for Shorebird Way has a value of 1, while the elements for all other streets have values of 0.

Figure 3. Mapping street address via one-hot encoding.

This approach effectively creates a Boolean variable for every feature value (e.g., street name). Here, if a house is on Shorebird Way then the binary value is 1 only for Shorebird Way. Thus, the model uses only the weight for Shorebird Way.

Similarly, if a house is at the corner of two streets, then two binary values are set to 1, and the model uses both their respective weights.

映射分类（枚举）值

分类特征具有一组离散的可能值。例如，名为 Lowland Countries 的特征只包含 3 个可能值：{'Netherlands', 'Belgium', 'Luxembourg'}

您可能会将分类特征（如 Lowland Countries）编码为枚举类型或表示不同值的整数离散集。例如：将荷兰表示为 0，将比利时表示为 1，将卢森堡表示为 2。

不过，机器学习模型通常将每个分类特征表示为单独的布尔值。例如，Lowland Countries 在模型中可以表示为 3 个单独的布尔值特征：x1：是荷兰吗？x2：是比利时吗？x3：是卢森堡吗？

采用这种方法编码还可以简化某个值可能属于多个分类这种情况（例如，“与法国接壤”对于比利时和卢森堡来说都是 True）。

One-hot encoding extends to numeric data that you do not want to directly multiply by a weight, such as a postal code.

Sparse Representation

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Suppose that you had 1,000,000 different street names in your data set that you wanted to include as values for street_name. Explicitly creating a binary vector of 1,000,000 elements where only 1 or 2 elements are true is a very inefficient representation in terms of both storage and computation time when processing these vectors.

In this situation, a common approach is to use a sparse representation in which only nonzero values are stored. In sparse representations, an independent model weight is still learned for each feature value, as described above.

Glossay

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1.discrete feature：A feature with a finite set of possible values. For example, a feature whose values may only be animal, vegetable, or mineral is a discrete (or categorical) feature. Contrast with continuous feature.

2.feature engineering：

The process of determining which features might be useful in training a model确定哪些特征可能在训练模型方面非常有用, and then converting raw data from log files and other sources into said features.然后将日志文件及其他来源的原始数据转换为所需的特征。In TensorFlow, feature engineering often means converting raw log file entries原始日志文件条目 to tf.Example protocol buffers.See also tf.Transform.Feature engineering is sometimes called feature extraction.

3.one-hot encoding：A sparse vector稀疏向量 in which:One element is set to 1.All other elements are set to 0.

One-hot encoding is commonly used to represent strings or identifiers字符串或标识符 that have a finite set of possible values.

For example, suppose a given botany data set chronicles 15,000 different species, each denoted with a unique string identifier. As part of feature engineering, you'll probably encode those string identifiers as one-hot vectors in which the vector has a size of 15,000.

4.representation：The process of mapping data to useful features.

5.sparse representation：A representation of a tensor that only stores nonzero elements.For example, the English language consists of about a million words. Consider two ways to represent a count of the words used in one English sentence:

• A dense representation of this sentence must set an integer for all one million cells, placing a 0 in most of them, and a low integer into a few of them.
• A sparse representation of this sentence stores only those cells symbolizing a word actually in the sentence. So, if the sentence contained only 20 unique words, then the sparse representation for the sentence would store an integer in only 20 cells.

For example, consider two ways to represent the sentence, "Dogs wag tails." As the following tables show, the dense representation consumes about a million cells; the sparse representation consumes only 3 cells:

Dense Representation

Cell Number	Word	Occurrence
0	a	0
1	aardvark	0
2	aargh	0
3	aarti	0
… 140,391 more words with an occurrence of 0
140395	dogs	1
… 633,062 words with an occurrence of 0
773458	tails	1
… 189,136 words with an occurrence of 0
962594	wag	1
… many more words with an occurrence of 0

Sparse Representation

Cell Number	Word	Occurrence
140395	dogs	1
773458	tails	1
962594	wag	1

Qualities of Good Features

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We've explored ways to map raw data into suitable feature vectors, but that's only part of the work. We must now explore what kinds of values actually make good features within those feature vectors.

Avoid rarely used discrete feature values

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Good feature values should appear more than 5 or so times in a data set. Doing so enables a model to learn how this feature value relates to the label. That is, having many examples with the same discrete value gives the model a chance to see the feature in different settings, and in turn, determine when it's a good predictor for the label. For example, a house_type feature would likely contain many examples in which its value was victorian:

✔This is a good example:
house_type: victorian

Conversely, if a feature's value appears only once or very rarely, the model can't make predictions based on that feature. For example, unique_house_id is a bad feature because each value would be used only once, so the model couldn't learn anything from it:

✘The following is an example of a unique value. This should be avoided.
unique_house_id: 8SK982ZZ1242Z

Prefer clear and obvious meanings

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Each feature should have a clear and obvious meaning to anyone on the project. For example, consider the following good feature for a house's age, which is instantly recognizable as the age in years:

✔The following is a good example of a clear value.
house_age: 27

Conversely, the meaning of the following feature value is pretty much indecipherable难以理解的 to anyone but the engineer who created it:

✘The following is an example of a value that is unclear. This should be avoided。
house_age: 851472000

In some cases, noisy data (rather than bad engineering choices) causes unclear values. For example, the following user_age came from a source that didn't check for appropriate values:

✘The following is an example of noisy/bad data. This should be avoided.
user_age: 277

Don't mix "magic" values with actual data

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Good floating-point features don't contain peculiar奇特 out-of-range discontinuities or "magic" values. For example, suppose a feature holds a floating-point value between 0 and 1. So, values like the following are fine:

✔The following is a good example:
quality_rating: 0.82
quality_rating: 0.37

However, if a user didn't enter a quality_rating, perhaps the data set represented its absence with a magic value like the following:

✘The following is an example of a magic value. This should be avoided.
quality_rating: -1

To work around magic values, convert the feature into two features:

• One feature holds only quality ratings, never magic values.
• One feature holds a boolean value indicating whether or not a quality_rating was supplied. Give this boolean feature a name like is_quality_rating_defined.

Account for upstream instability上游不稳定性

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The definition of a feature shouldn't change over time. For example, the following value is useful because the city name probably won't change. (Note that we'll still need to convert a string like "br/sao_paulo" to a one-hot vector.)

✔This is a good example:
city_id: "br/sao_paulo"

But gathering a value inferred by another model carries additional costs. Perhaps the value "219" currently represents Sao Paulo, but that representation could easily change on a future run of the other model:

✘The following is an example of a value that could change. This should be avoided.
inferred_city_cluster: "219"

Cleaning Data

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Apple trees produce some mixture of great fruit and wormy messes. Yet the apples in high-end grocery stores display 100% perfect fruit. Between orchard果园 and grocery, someone spends significant time removing the bad apples or throwing a little wax on the salvageable挽救 ones. As an ML engineer, you'll spend enormous amounts of your time tossing out折腾 bad examples and cleaning up the salvageable ones. Even a few "bad apples" can spoil a large data set.

Scaling feature values

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Scaling缩放 means converting floating-point feature values from their natural range (for example, 100 to 900) into a standard range (for example, 0 to 1 or -1 to +1). If a feature set consists of only a single feature, then scaling provides little to no practical benefit. If, however, a feature set consists of multiple features, then feature scaling provides the following benefits:

• Helps gradient descent converge汇合 more quickly.
• Helps avoid the "NaN trap," in which one number in the model becomes a NaN (e.g., when a value exceeds the floating-point precision limit during training), and—due to math operations—every other number in the model also eventually becomes a NaN.
• Helps the model learn appropriate weights for each feature. Without feature scaling, the model will pay too much attention to the features having a wider range.

You don't have to give every floating-point feature exactly the same scale. Nothing terrible will happen if Feature A is scaled from -1 to +1 while Feature B is scaled from -3 to +3. However, your model will react poorly if Feature B is scaled from 5000 to 100000.

Learn more about scaling

One obvious way to scale numerical data is to linearly map [min value, max value] to a small scale, such as [-1, +1].

Another popular scaling tactic is to calculate the Z score of each value. The Z score relates the number of standard deviations away from the mean. In other words:

scaledvalue=(value−mean)/stddev.

For example, given:

• mean = 100
• standard deviation = 20
• original value = 130

then:

  scaled_value = (130 - 100) / 20
  scaled_value = 1.5

Scaling with Z scores means that most scaled values will be between -3 and +3, but a few values will be a little higher or lower than that range.

Handling extreme outliers

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The following plot represents a feature called roomsPerPerson from the California Housing data set. The value of roomsPerPerson was calculated by dividing the total number of rooms for an area by the population for that area. The plot shows that the vast majority of areas in California have one or two rooms per person. But take a look along the x-axis.

Figure 4. A verrrrry lonnnnnnng tail.

How could we minimize the influence of those extreme outliers? Well, one way would be to take the log of every value:

Figure 5. Logarithmic scaling对数缩放 still leaves a tail.

Log scaling does a slightly better job, but there's still a significant tail of outlier values. Let's pick yet another approach. What if we simply "cap" or "clip" the maximum value of roomsPerPerson at an arbitrary value, say 4.0?

Figure 6. Clipping feature values at 4.0

Clipping the feature value at 4.0 doesn't mean that we ignore all values greater than 4.0. Rather, it means that all values that were greater than 4.0 now become 4.0. This explains the funny hill at 4.0. Despite that hill, the scaled feature set is now more useful than the original data.

Binning分档

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The following plot shows the relative prevalence流行 of houses at different latitudes in California. Notice the clustering—Los Angeles is about at latitude 34 and San Francisco is roughly at latitude 38.

Figure 7. Houses per latitude.

In the data set, latitude is a floating-point value. However, it doesn't make sense to represent latitude as a floating-point feature in our model. That's because no linear relationship exists between latitude and housing values. For example, houses in latitude 35 are not 35/34 more expensive (or less expensive) than houses at latitude 34. And yet, individual latitudes probably are a pretty good predictor of house values.

To make latitude a helpful predictor, let's divide latitudes into "bins" as suggested by the following figure:

Figure 8. Binning values.

Instead of having one floating-point feature, we now have 11 distinct boolean features (LatitudeBin1, LatitudeBin2, ..., LatitudeBin11). Having 11 separate features is somewhat inelegant, so let's unite them into a single 11-element vector. Doing so will enable us to represent latitude 37.4 as follows:[0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]

Thanks to binning, our model can now learn completely different weights for each latitude.

Learn more about binning boundaries

For simplicity's sake in the latitude example, we used whole numbers as bin boundaries. Had we wanted finer-grain resolution, we could have split bin boundaries at, say, every tenth of十分之一 a degree. Adding more bins enables the model to learn different behaviors from latitude 37.4 than latitude 37.5, but only if there are sufficient examples at each tenth of a latitude.

Another approach is to bin by quantile分位数, which ensures that the number of examples in each bucket is equal. Binning by quantile completely removes the need to worry about outliers.

Scrubbing

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Until now, we've assumed that all the data used for training and testing was trustworthy. In real-life, many examples in data sets are unreliable due to one or more of the following:

• Omitted values. For instance, a person forgot to enter a value for a house's age.
• Duplicate examples. For example, a server mistakenly uploaded the same logs twice.
• Bad labels. For instance, a person mislabeled a picture of an oak tree as a maple.
• Bad feature values. For example, someone typed in an extra digit, or a thermometer was left out in the sun.

Once detected, you typically "fix" bad examples by removing them from the data set. To detect omitted values or duplicated examples, you can write a simple program. Detecting bad feature values or labels can be far trickier.

In addition to detecting bad individual examples, you must also detect bad data in the aggregate. Histograms are a great mechanism机制 for visualizing your data in the aggregate. In addition, getting statistics like the following can help:

• Maximum and minimum
• Mean and median
• Standard deviation

Consider generating lists of the most common values for discrete features. For example, do the number of examples with country:uk match the number you expect. Should language:jp really be the most common language in your data set?

Know your data

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Follow these rules:

• Keep in mind what you think your data should look like.
• Verify that the data meets these expectations (or that you can explain why it doesn’t).
• Double-check that the training data agrees with other sources (for example, dashboards).

Treat your data with all the care that you would treat any mission-critical code. Good ML relies on good data.

Additional Information

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Rules of Machine Learning, ML Phase II: Feature Engineering

Glossay

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1. binning：See bucketing.
2. bucketing：Converting a (usually continuous) feature into multiple binary features called buckets or bins, typically based on value range. For example, instead of representing temperature as a single continuous floating-point feature, you could chop ranges of temperatures into discrete bins. Given temperature data sensitive to a tenth of a degree, all temperatures between 0.0 and 15.0 degrees could be put into one bin, 15.1 to 30.0 degrees could be a second bin, and 30.1 to 50.0 degrees could be a third bin.
3. NaN trap：When one number in your model becomes a NaN during training, which causes many or all other numbers in your model to eventually become a NaN.NaN is an abbreviation for "Not a Number."
4. scaling：A commonly used practice in feature engineering to tame a feature's range of values to match the range of other features in the data set. For example, suppose that you want all floating-point features in the data set to have a range of 0 to 1. Given a particular feature's range of 0 to 500, you could scale that feature by dividing each value by 500.See also normalization.
5. normalization：The process of converting an actual range of values into a standard range of values, typically -1 to +1 or 0 to 1. For example, suppose the natural range of a certain feature is 800 to 6,000. Through subtraction and division, you can normalize those values into the range -1 to +1.See also scaling.
6. feature set：The group of features your machine learning model trains on. For example, postal code, property size, and property condition might comprise a simple feature set for a model that predicts housing prices.
7. outliers：Values distant from most other values. In machine learning, any of the following are outliers:1.Weights with high absolute values高绝对值.2.Predicted values relatively far away from the actual values.3.Input data whose values are more than roughly 3 standard deviations 三个标准差from the mean.  Outliers often cause problems in model training.

Programming Exercise

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In this programming exercise, you'll create a good, minimal set of features.