Aggregators

The aggregators module is exposed as hl.agg, e.g. hl.agg.sum.

collect(expr) Collect records into an array.
collect_as_set(expr) Collect records into a set.
count() Count the number of records.
count_where(condition) Count the number of records where a predicate is True.
counter(expr) Count the occurrences of each unique record and return a dictionary.
any(condition) Returns True if condition is True for any record.
all(condition) Returns True if condition is True for every record.
take(expr, n[, ordering]) Take n records of expr, optionally ordered by ordering.
min(expr) Compute the minimum expr.
max(expr) Compute the maximum expr.
sum(expr) Compute the sum of all records of expr.
array_sum(expr) Compute the coordinate-wise sum of all records of expr.
mean(expr) Compute the mean value of records of expr.
stats(expr) Compute a number of useful statistics about expr.
product(expr) Compute the product of all records of expr.
fraction(predicate) Compute the fraction of records where predicate is True.
hardy_weinberg_test(expr) Performs test of Hardy-Weinberg equilibrium.
explode(f, array_agg_expr) Explode an array or set expression to aggregate the elements of all records.
filter(condition, aggregation) Filter records according to a predicate.
inbreeding(expr, prior) Compute inbreeding statistics on calls.
call_stats(call, alleles) Compute useful call statistics.
info_score(gp) Compute the IMPUTE information score.
hist(expr, start, end, bins) Compute binned counts of a numeric expression.
linreg(y, x[, nested_dim, weight]) Compute multivariate linear regression statistics.
corr(x, y) Computes the Pearson correlation coefficient between x and y.
group_by(group, agg_expr) Compute aggregation statistics stratified by one or more groups.
downsample(x, y[, label, n_divisions]) Downsample (x, y) coordinate datapoints.
hail.expr.aggregators.collect(expr) → hail.expr.expressions.typed_expressions.ArrayExpression[source]

Collect records into an array.

Examples

Collect the ID field where HT is greater than 68:

>>> table1.aggregate(agg.filter(table1.HT > 68, agg.collect(table1.ID)))
[2, 3]

Notes

The element order of the resulting array is not guaranteed, and in some cases is non-deterministic.

Use collect_as_set() to collect unique items.

Warning

Collecting a large number of items can cause out-of-memory exceptions.

Parameters:expr (Expression) – Expression to collect.
Returns:ArrayExpression – Array of all expr records.
hail.expr.aggregators.collect_as_set(expr) → hail.expr.expressions.typed_expressions.SetExpression[source]

Collect records into a set.

Examples

Collect the unique ID field where HT is greater than 68:

>>> table1.aggregate(agg.filter(table1.HT > 68, agg.collect_as_set(table1.ID)))
{2, 3}

Warning

Collecting a large number of items can cause out-of-memory exceptions.

Parameters:expr (Expression) – Expression to collect.
Returns:SetExpression – Set of unique expr records.
hail.expr.aggregators.count() → hail.expr.expressions.typed_expressions.Int64Expression[source]

Count the number of records.

Examples

Group by the SEX field and count the number of rows in each category:

>>> (table1.group_by(table1.SEX)
...        .aggregate(n=agg.count())
...        .show())
+-----+-------+
| SEX |     n |
+-----+-------+
| str | int64 |
+-----+-------+
| "F" |     2 |
| "M" |     2 |
+-----+-------+
Returns:Expression of type tint64 – Total number of records.
hail.expr.aggregators.count_where(condition) → hail.expr.expressions.typed_expressions.Int64Expression[source]

Count the number of records where a predicate is True.

Examples

Count the number of individuals with HT greater than 68:

>>> table1.aggregate(agg.count_where(table1.HT > 68))
2
Parameters:condition (BooleanExpression) – Criteria for inclusion.
Returns:Expression of type tint64 – Total number of records where condition is True.
hail.expr.aggregators.counter(expr) → hail.expr.expressions.typed_expressions.DictExpression[source]

Count the occurrences of each unique record and return a dictionary.

Examples

Count the number of individuals for each unique SEX value:

>>> table1.aggregate(agg.counter(table1.SEX))  
{'M': 2L, 'F': 2L}

Notes

This aggregator method returns a dict expression whose key type is the same type as expr and whose value type is Expression of type tint64. This dict contains a key for each unique value of expr, and the value is the number of times that key was observed.

Ensure that the result can be stored in memory on a single machine.

Warning

Using counter() with a large number of unique items can cause out-of-memory exceptions.

Parameters:expr (Expression) – Expression to count by key.
Returns:DictExpression – Dictionary with the number of occurrences of each unique record.
hail.expr.aggregators.any(condition) → hail.expr.expressions.typed_expressions.BooleanExpression[source]

Returns True if condition is True for any record.

Examples

>>> (table1.group_by(table1.SEX)
... .aggregate(any_over_70 = agg.any(table1.HT > 70))
... .show())
+-----+-------------+
| SEX | any_over_70 |
+-----+-------------+
| str | bool        |
+-----+-------------+
| "F" | false       |
| "M" | true        |
+-----+-------------+

Notes

If there are no records to aggregate, the result is False.

Missing records are not considered. If every record is missing, the result is also False.

Parameters:condition (BooleanExpression) – Condition to test.
Returns:BooleanExpression
hail.expr.aggregators.all(condition) → hail.expr.expressions.typed_expressions.BooleanExpression[source]

Returns True if condition is True for every record.

Examples

>>> (table1.group_by(table1.SEX)
... .aggregate(all_under_70 = agg.all(table1.HT < 70))
... .show())
+-----+--------------+
| SEX | all_under_70 |
+-----+--------------+
| str | bool         |
+-----+--------------+
| "F" | false        |
| "M" | false        |
+-----+--------------+

Notes

If there are no records to aggregate, the result is True.

Missing records are not considered. If every record is missing, the result is also True.

Parameters:condition (BooleanExpression) – Condition to test.
Returns:BooleanExpression
hail.expr.aggregators.take(expr, n, ordering=None) → hail.expr.expressions.typed_expressions.ArrayExpression[source]

Take n records of expr, optionally ordered by ordering.

Examples

Take 3 elements of field X:

>>> table1.aggregate(agg.take(table1.X, 3))
[5, 6, 7]

Take the ID and HT fields, ordered by HT (descending):

>>> table1.aggregate(agg.take(hl.struct(ID=table1.ID, HT=table1.HT),
...                           3,
...                           ordering=-table1.HT))
[Struct(ID=2, HT=72), Struct(ID=3, HT=70), Struct(ID=1, HT=65)]

Notes

The resulting array can include fewer than n elements if there are fewer than n total records.

The ordering argument may be an expression, a function, or None.

If ordering is an expression, this expression’s type should be one with a natural ordering (e.g. numeric).

If ordering is a function, it will be evaluated on each record of expr to compute the value used for ordering. In the above example, ordering=-table1.HT and ordering=lambda x: -x.HT would be equivalent.

If ordering is None, then there is no guaranteed ordering on the elements taken, and and the results may be non-deterministic.

Missing values are always sorted last.

Parameters:
Returns:

ArrayExpression – Array of up to n records of expr.

hail.expr.aggregators.min(expr) → hail.expr.expressions.typed_expressions.NumericExpression[source]

Compute the minimum expr.

Examples

Compute the minimum value of HT:

>>> table1.aggregate(agg.min(table1.HT))
60

Notes

This method returns the minimum non-missing value. If there are no non-missing values, then the result is missing.

Parameters:expr (NumericExpression) – Numeric expression.
Returns:NumericExpression – Minimum value of all expr records, same type as expr.
hail.expr.aggregators.max(expr) → hail.expr.expressions.typed_expressions.NumericExpression[source]

Compute the maximum expr.

Examples

Compute the maximum value of HT:

>>> table1.aggregate(agg.max(table1.HT))
72

Notes

This method returns the maximum non-missing value. If there are no non-missing values, then the result is missing.

Parameters:expr (NumericExpression) – Numeric expression.
Returns:NumericExpression – Maximum value of all expr records, same type as expr.
hail.expr.aggregators.sum(expr)[source]

Compute the sum of all records of expr.

Examples

Compute the sum of field C1:

>>> table1.aggregate(agg.sum(table1.C1))
25

Notes

Missing values are ignored (treated as zero).

If expr is an expression of type tint32, tint64, or tbool, then the result is an expression of type tint64. If expr is an expression of type tfloat32 or tfloat64, then the result is an expression of type tfloat64.

Warning

Boolean values are cast to integers before computing the sum.

Parameters:expr (NumericExpression) – Numeric expression.
Returns:Expression of type tint64 or tfloat64 – Sum of records of expr.
hail.expr.aggregators.array_sum(expr) → hail.expr.expressions.typed_expressions.ArrayExpression[source]

Compute the coordinate-wise sum of all records of expr.

Examples

Compute the sum of C1 and C2:

>>> table1.aggregate(agg.array_sum([table1.C1, table1.C2]))
[25, 282]

Notes

All records must have the same length. Each coordinate is summed independently as described in sum().

Parameters:expr (ArrayNumericExpression)
Returns:ArrayExpression with element type tint64 or tfloat64
hail.expr.aggregators.mean(expr) → hail.expr.expressions.typed_expressions.Float64Expression[source]

Compute the mean value of records of expr.

Examples

Compute the mean of field HT:

>>> table1.aggregate(agg.mean(table1.HT))
66.75

Notes

Missing values are ignored.

Parameters:expr (NumericExpression) – Numeric expression.
Returns:Expression of type tfloat64 – Mean value of records of expr.
hail.expr.aggregators.stats(expr) → hail.expr.expressions.typed_expressions.StructExpression[source]

Compute a number of useful statistics about expr.

Examples

Compute statistics about field HT:

>>> table1.aggregate(agg.stats(table1.HT))
Struct(mean=66.75, stdev=4.656984002549289, min=60.0, max=72.0, n=4, sum=267.0)

Notes

Computes a struct with the following fields:

Parameters:expr (NumericExpression) – Numeric expression.
Returns:StructExpression – Struct expression with fields mean, stdev, min, max, n, and sum.
hail.expr.aggregators.product(expr)[source]

Compute the product of all records of expr.

Examples

Compute the product of field C1:

>>> table1.aggregate(agg.product(table1.C1))
440

Notes

Missing values are ignored (treated as one).

If expr is an expression of type tint32, tint64 or tbool, then the result is an expression of type tint64. If expr is an expression of type tfloat32 or tfloat64, then the result is an expression of type tfloat64.

Warning

Boolean values are cast to integers before computing the product.

Parameters:expr (NumericExpression) – Numeric expression.
Returns:Expression of type tint64 or tfloat64 – Product of records of expr.
hail.expr.aggregators.fraction(predicate) → hail.expr.expressions.typed_expressions.Float64Expression[source]

Compute the fraction of records where predicate is True.

Examples

Compute the fraction of rows where SEX is “F” and HT > 65:

>>> table1.aggregate(agg.fraction((table1.SEX == 'F') & (table1.HT > 65)))
0.25

Notes

Missing values for predicate are treated as False.

Parameters:predicate (BooleanExpression) – Boolean predicate.
Returns:Expression of type tfloat64 – Fraction of records where predicate is True.
hail.expr.aggregators.hardy_weinberg_test(expr) → hail.expr.expressions.typed_expressions.StructExpression[source]

Performs test of Hardy-Weinberg equilibrium.

Examples

Test each row of a dataset:

>>> dataset_result = dataset.annotate_rows(hwe = agg.hardy_weinberg_test(dataset.GT))

Test each row on a sub-population:

>>> dataset_result = dataset.annotate_rows(
...     hwe_eas = agg.filter(dataset.pop == 'EAS',
...                          agg.hardy_weinberg_test(dataset.GT)))

Notes

This method performs the test described in functions.hardy_weinberg_test() based solely on the counts of homozygous reference, heterozygous, and homozygous variant calls.

The resulting struct expression has two fields:

  • het_freq_hwe (tfloat64) - Expected frequency of heterozygous calls under Hardy-Weinberg equilibrium.
  • p_value (tfloat64) - p-value from test of Hardy-Weinberg equilibrium.

Hail computes the exact p-value with mid-p-value correction, i.e. the probability of a less-likely outcome plus one-half the probability of an equally-likely outcome. See this document for details on the Levene-Haldane distribution and references.

Warning

Non-diploid calls (ploidy != 2) are ignored in the counts. While the counts are defined for multiallelic variants, this test is only statistically rigorous in the biallelic setting; use split_multi() to split multiallelic variants beforehand.

Parameters:expr (CallExpression) – Call to test for Hardy-Weinberg equilibrium.
Returns:StructExpression – Struct expression with fields het_freq_hwe and p_value.
hail.expr.aggregators.explode(f, array_agg_expr) → hail.expr.expressions.base_expression.Expression[source]

Explode an array or set expression to aggregate the elements of all records.

Examples

Compute the mean of all elements in fields C1, C2, and C3:

>>> table1.aggregate(agg.explode(lambda elt: agg.mean(elt), [table1.C1, table1.C2, table1.C3]))
24.833333333333332

Compute the set of all observed elements in the filters field (Set[String]):

>>> dataset.aggregate_rows(agg.explode(lambda elt: agg.collect_as_set(elt), dataset.filters))
{'VQSRTrancheINDEL97.00to99.00'}

Notes

This method can be used with aggregator functions to aggregate the elements of collection types (tarray and tset).

Parameters:
Returns:

Expression – Aggregation expression.

hail.expr.aggregators.filter(condition, aggregation) → hail.expr.expressions.base_expression.Expression[source]

Filter records according to a predicate.

Examples

Collect the ID field where HT >= 70:

>>> table1.aggregate(agg.filter(table1.HT >= 70, agg.collect(table1.ID)))
[2, 3]

Notes

This method can be used with aggregator functions to remove records from aggregation.

Parameters:
Returns:

Aggregable – Aggregable expression.

hail.expr.aggregators.inbreeding(expr, prior) → hail.expr.expressions.typed_expressions.StructExpression[source]

Compute inbreeding statistics on calls.

Examples

Compute inbreeding statistics per column:

>>> dataset_result = dataset.annotate_cols(IB = agg.inbreeding(dataset.GT, dataset.variant_qc.AF[1]))
>>> dataset_result.IB.show()
+------------------+-----------+-------------+------------------+------------------+
| s                | IB.f_stat | IB.n_called | IB.expected_homs | IB.observed_homs |
+------------------+-----------+-------------+------------------+------------------+
| str              |   float64 |       int64 |          float64 |            int64 |
+------------------+-----------+-------------+------------------+------------------+
| "C1046::HG02024" |  3.88e-01 |          12 |         1.04e+01 |               11 |
| "C1046::HG02025" |  3.99e-01 |          13 |         1.13e+01 |               12 |
| "C1046::HG02026" |  3.88e-01 |          12 |         1.04e+01 |               11 |
| "C1047::HG00731" | -1.31e+00 |          12 |         1.07e+01 |                9 |
| "C1047::HG00732" |  1.00e+00 |          12 |         1.04e+01 |               12 |
| "C1047::HG00733" | -8.04e-01 |          13 |         1.13e+01 |               10 |
| "C1048::HG02024" |  3.88e-01 |          12 |         1.04e+01 |               11 |
| "C1048::HG02025" |  3.99e-01 |          13 |         1.13e+01 |               12 |
| "C1048::HG02026" |  1.00e+00 |          12 |         1.04e+01 |               12 |
| "C1049::HG00731" | -1.41e+00 |          13 |         1.13e+01 |                9 |
+------------------+-----------+-------------+------------------+------------------+
showing top 10 rows

Notes

E is total number of expected homozygous calls, given by the sum of 1 - 2.0 * prior * (1 - prior) across records.

O is the observed number of homozygous calls across records.

N is the number of non-missing calls.

F is the inbreeding coefficient, and is computed by: (O - E) / (N - E).

This method returns a struct expression with four fields:

  • f_stat (tfloat64): F, the inbreeding coefficient.
  • n_called (tint64): N, the number of non-missing calls.
  • expected_homs (tfloat64): E, the expected number of homozygotes.
  • observed_homs (tint64): O, the number of observed homozygotes.
Parameters:
Returns:

StructExpression – Struct expression with fields f_stat, n_called, expected_homs, observed_homs.

hail.expr.aggregators.call_stats(call, alleles) → hail.expr.expressions.typed_expressions.StructExpression[source]

Compute useful call statistics.

Examples

Compute call statistics per row:

>>> dataset_result = dataset.annotate_rows(gt_stats = agg.call_stats(dataset.GT, dataset.alleles))
>>> dataset_result.rows().key_by('locus').select('gt_stats').show()
+---------------+--------------+---------------------+-------------+
| locus         | gt_stats.AC  | gt_stats.AF         | gt_stats.AN |
+---------------+--------------+---------------------+-------------+
| locus<GRCh37> | array<int32> | array<float64>      |       int32 |
+---------------+--------------+---------------------+-------------+
| 20:12990057   | [148,52]     | [7.40e-01,2.60e-01] |         200 |
| 20:13029862   | [0,198]      | [0.00e+00,1.00e+00] |         198 |
| 20:13074235   | [13,187]     | [6.50e-02,9.35e-01] |         200 |
| 20:13140720   | [194,6]      | [9.70e-01,3.00e-02] |         200 |
| 20:13695498   | [175,25]     | [8.75e-01,1.25e-01] |         200 |
| 20:13714384   | [199,1]      | [9.95e-01,5.00e-03] |         200 |
| 20:13765944   | [132,2]      | [9.85e-01,1.49e-02] |         134 |
| 20:13765954   | [180,2]      | [9.89e-01,1.10e-02] |         182 |
| 20:13845987   | [2,198]      | [1.00e-02,9.90e-01] |         200 |
| 20:16223957   | [145,45]     | [7.63e-01,2.37e-01] |         190 |
+---------------+--------------+---------------------+-------------+

+---------------------------+
| gt_stats.homozygote_count |
+---------------------------+
| array<int32>              |
+---------------------------+
| [57,9]                    |
| [0,99]                    |
| [1,88]                    |
| [95,1]                    |
| [75,0]                    |
| [99,0]                    |
| [65,0]                    |
| [89,0]                    |
| [0,98]                    |
| [64,14]                   |
+---------------------------+
showing top 10 rows

Notes

This method is meaningful for computing call metrics per variant, but not especially meaningful for computing metrics per sample.

This method returns a struct expression with three fields:

  • AC (tarray of tint32) - Allele counts. One element for each allele, including the reference.
  • AF (tarray of tfloat64) - Allele frequencies. One element for each allele, including the reference.
  • AN (tint32) - Allele number. The total number of called alleles, or the number of non-missing calls * 2.
  • homozygote_count (tarray of tint32) - Homozygote genotype counts for each allele, including the reference. Only diploid genotype calls are counted.
Parameters:
  • call (CallExpression)
  • alleles (ArrayStringExpression) – Variant alleles.
Returns:

StructExpression – Struct expression with fields AC, AF, AN, and homozygote_count.

hail.expr.aggregators.info_score(gp) → hail.expr.expressions.typed_expressions.StructExpression[source]

Compute the IMPUTE information score.

Examples

Calculate the info score per variant:

>>> gen_mt = hl.import_gen('data/example.gen', sample_file='data/example.sample')
>>> gen_mt = gen_mt.annotate_rows(info_score = hl.agg.info_score(gen_mt.GP))

Calculate group-specific info scores per variant:

>>> gen_mt = hl.import_gen('data/example.gen', sample_file='data/example.sample')
>>> gen_mt = gen_mt.annotate_cols(is_case = hl.rand_bool(0.5))
>>> gen_mt = gen_mt.annotate_rows(info_score = hl.agg.group_by(gen_mt.is_case, hl.agg.info_score(gen_mt.GP)))

Notes

The result of info_score() is a struct with two fields:

  • score (float64) – Info score.
  • n_included (int32) – Number of non-missing samples included in the calculation.

We implemented the IMPUTE info measure as described in the supplementary information from Marchini & Howie. Genotype imputation for genome-wide association studies. Nature Reviews Genetics (2010). To calculate the info score \(I_{A}\) for one SNP:

\[\begin{split}I_{A} = \begin{cases} 1 - \frac{\sum_{i=1}^{N}(f_{i} - e_{i}^2)}{2N\hat{\theta}(1 - \hat{\theta})} & \text{when } \hat{\theta} \in (0, 1) \\ 1 & \text{when } \hat{\theta} = 0, \hat{\theta} = 1\\ \end{cases}\end{split}\]
  • \(N\) is the number of samples with imputed genotype probabilities [\(p_{ik} = P(G_{i} = k)\) where \(k \in \{0, 1, 2\}\)]
  • \(e_{i} = p_{i1} + 2p_{i2}\) is the expected genotype per sample
  • \(f_{i} = p_{i1} + 4p_{i2}\)
  • \(\hat{\theta} = \frac{\sum_{i=1}^{N}e_{i}}{2N}\) is the MLE for the population minor allele frequency

Hail will not generate identical results to QCTOOL for the following reasons:

  • Hail automatically removes genotype probability distributions that do not meet certain requirements on data import with import_gen() and import_bgen().
  • Hail does not use the population frequency to impute genotype probabilities when a genotype probability distribution has been set to missing.
  • Hail calculates the same statistic for sex chromosomes as autosomes while QCTOOL incorporates sex information.
  • The floating point number Hail stores for each genotype probability is slightly different than the original data due to rounding and normalization of probabilities.

Warning

  • The info score Hail reports will be extremely different from QCTOOL when a SNP has a high missing rate.
  • If the gp array must contain 3 elements, and its elements may not be missing.
  • If the genotype data was not imported using the import_gen() or import_bgen() functions, then the results for all variants will be score = NA and n_included = 0.
  • It only makes semantic sense to compute the info score per variant. While the aggregator will run in any context if its arguments are the right type, the results are only meaningful in a narrow context.
Parameters:gp (ArrayNumericExpression) – Genotype probability array. Must have 3 elements, all of which must be defined.
Returns:StructExpression – Struct with fields score and n_included.
hail.expr.aggregators.hist(expr, start, end, bins) → hail.expr.expressions.typed_expressions.StructExpression[source]

Compute binned counts of a numeric expression.

Examples

Compute a histogram of field GQ:

>>> dataset.aggregate_entries(agg.hist(dataset.GQ, 0, 100, 10))  
Struct(bin_edges=[0.0, 10.0, 20.0, 30.0, 40.0, 50.0, 60.0, 70.0, 80.0, 90.0, 100.0],
       bin_freq=[2194L, 637L, 2450L, 1081L, 518L, 402L, 11168L, 1918L, 1379L, 11973L]),
       n_smaller=0,
       n_greater=0)

Notes

This method returns a struct expression with four fields:

  • bin_edges (tarray of tfloat64): Bin edges. Bin i contains values in the left-inclusive, right-exclusive range [ bin_edges[i], bin_edges[i+1] ).
  • bin_freq (tarray of tint64): Bin frequencies. The number of records found in each bin.
  • n_smaller (tint64): The number of records smaller than the start of the first bin.
  • n_larger (tint64): The number of records larger than the end of the last bin.
Parameters:
  • expr (NumericExpression) – Target numeric expression.
  • start (int or float) – Start of histogram range.
  • end (int or float) – End of histogram range.
  • bins (int or float) – Number of bins.
Returns:

StructExpression – Struct expression with fields bin_edges, bin_freq, n_smaller, and n_larger.

hail.expr.aggregators.linreg(y, x, nested_dim=1, weight=None) → hail.expr.expressions.typed_expressions.StructExpression[source]

Compute multivariate linear regression statistics.

Examples

Regress HT against an intercept (1), SEX, and C1:

>>> table1.aggregate(agg.linreg(table1.HT, [1, table1.SEX == 'F', table1.C1]))  
Struct(beta=[88.50000000000014, 81.50000000000057, -10.000000000000068],
       standard_error=[14.430869689661844, 59.70552738231206, 7.000000000000016],
       t_stat=[6.132686518775844, 1.365032746099571, -1.428571428571435],
       p_value=[0.10290201427537926, 0.40250974549499974, 0.3888002244284281],
       multiple_standard_error=4.949747468305833,
       multiple_r_squared=0.7175792507204611,
       adjusted_r_squared=0.1527377521613834,
       f_stat=1.2704081632653061,
       multiple_p_value=0.5314327326007864,
       n=4)

Regress blood pressure against an intercept (1), genotype, age, and the interaction of genotype and age:

>>> ds_ann = ds.annotate_rows(linreg =
...     hl.agg.linreg(ds.pheno.blood_pressure,
...                   [1,
...                    ds.GT.n_alt_alleles(),
...                    ds.pheno.age,
...                    ds.GT.n_alt_alleles() * ds.pheno.age]))

Warning

As in the example, the intercept covariate 1 must be included explicitly if desired.

Notes

In relation to lm.summary in R, linreg(y, x = [1, mt.x1, mt.x2]) computes summary(lm(y ~ x1 + x2)) and linreg(y, x = [mt.x1, mt.x2], nested_dim=0) computes summary(lm(y ~ x1 + x2 - 1)).

More generally, nested_dim defines the number of effects to fit in the nested (null) model, with the effects on the remaining covariates fixed to zero.

The returned struct has ten fields:
  • beta (tarray of tfloat64): Estimated regression coefficient for each covariate.
  • standard_error (tarray of tfloat64): Estimated standard error for each covariate.
  • t_stat (tarray of tfloat64): t-statistic for each covariate.
  • p_value (tarray of tfloat64): p-value for each covariate.
  • multiple_standard_error (tfloat64): Estimated standard deviation of the random error.
  • multiple_r_squared (tfloat64): Coefficient of determination for nested models.
  • adjusted_r_squared (tfloat64): Adjusted multiple_r_squared taking into account degrees of freedom.
  • f_stat (tfloat64): F-statistic for nested models.
  • multiple_p_value (tfloat64): p-value for the F-test of nested models.
  • n (tint64): Number of samples included in the regression. A sample is included if and only if y, all elements of x, and weight (if set) are non-missing.

All but the last field are missing if n is less than or equal to the number of covariates or if the covariates are linearly dependent.

If set, the weight parameter generalizes the model to weighted least squares, useful for heteroscedastic (diagonal but non-constant) variance.

Warning

If any weight is negative, the resulting statistics will be nan.

Parameters:
  • y (Float64Expression) – Response (dependent variable).
  • x (Float64Expression or list of Float64Expression) – Covariates (independent variables).
  • nested_dim (int) – The null model includes the first nested_dim covariates. Must be between 0 and k (the length of x).
  • weight (Float64Expression, optional) – Non-negative weight for weighted least squares.
Returns:

StructExpression – Struct of regression results.

hail.expr.aggregators.corr(x, y) → hail.expr.expressions.typed_expressions.Float64Expression[source]

Computes the Pearson correlation coefficient between x and y.

Examples

>>> ds.aggregate_cols(hl.agg.corr(ds.pheno.age, ds.pheno.blood_pressure))  
0.16592876044845484

Notes

Only records where both x and y are non-missing will be included in the calculation.

In the case that there are no non-missing pairs, the result will be missing.

See also

linreg()

Parameters:
Returns:

Float64Expression

hail.expr.aggregators.group_by(group, agg_expr) → hail.expr.expressions.typed_expressions.DictExpression[source]

Compute aggregation statistics stratified by one or more groups.

Danger

This functionality is experimental. It may not be tested as well as other parts of Hail and the interface is subject to change.

Examples

Compute linear regression statistics stratified by SEX:

>>> table1.aggregate(agg.group_by(table1.SEX,
...                               agg.linreg(table1.HT, table1.C1, nested_dim=0)))  
{
'F': Struct(beta=[6.153846153846154],
            standard_error=[0.7692307692307685],
            t_stat=[8.000000000000009],
            p_value=[0.07916684832113098],
            multiple_standard_error=11.4354374979373,
            multiple_r_squared=0.9846153846153847,
            adjusted_r_squared=0.9692307692307693,
            f_stat=64.00000000000014,
            multiple_p_value=0.07916684832113098,
            n=2),
'M': Struct(beta=[34.25],
            standard_error=[1.75],
            t_stat=[19.571428571428573],
            p_value=[0.03249975499062629],
            multiple_standard_error=4.949747468305833,
            multiple_r_squared=0.9973961101073441,
            adjusted_r_squared=0.9947922202146882,
            f_stat=383.0408163265306,
            multiple_p_value=0.03249975499062629,
            n=2)
}

Compute call statistics stratified by population group and case status:

>>> ann = ds.annotate_rows(call_stats=hl.agg.group_by(hl.struct(pop=ds.pop, is_case=ds.is_case),
...                                                   hl.agg.call_stats(ds.GT, ds.alleles)))
Parameters:
  • group (Expression or list of Expression) – Group to stratify the result by.
  • agg_expr (Expression) – Aggregation or scan expression to compute per grouping.
Returns:

DictExpression – Dictionary where the keys are group and the values are the result of computing agg_expr for each unique value of group.

hail.expr.aggregators.downsample(x, y, label=None, n_divisions=500) → hail.expr.expressions.typed_expressions.ArrayExpression[source]

Downsample (x, y) coordinate datapoints.

Parameters:
Returns:

ArrayExpression – Expression for downsampled coordinate points (x, y). The element type of the array is ttuple of tfloat64, tfloat64, and tarray of tstring