Skip to content

metric

Computes various statistical metrics based on the specified metric name.

Parameters:

Name Type Description Default
metric_name str

The name of the metric to compute. Options include 'mean', 'variance', 'entropy', 'skewness', etc.

 required
x Tensor

The input tensor.

 required

Returns:

Type Description
Tensor

The computed metric.

Raises:

Type Description
ValueError

If the metric name is not recognized or the input tensor is invalid.
Source code in tinybig/koala/statistics/metric.py 
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
def metric(
    metric_name: str,
    x: torch.Tensor,
    *args, **kwargs
):
    """
    Computes various statistical metrics based on the specified metric name.

    Parameters
    ----------
    metric_name : str
        The name of the metric to compute. Options include 'mean', 'variance',
        'entropy', 'skewness', etc.
    x : torch.Tensor
        The input tensor.

    Returns
    -------
    torch.Tensor
        The computed metric.

    Raises
    ------
    ValueError
        If the metric name is not recognized or the input tensor is invalid.
    """
    assert x is not None and metric_name is not None
    match metric_name:
        case 'mean': return mean(x=x)
        case 'batch_mean': return batch_mean(x=x, *args, **kwargs)
        case 'weighted_mean' | 'wmean': return weighted_mean(x=x, *args, **kwargs)
        case 'batch_weighted_mean' | 'batch_wmean': return batch_weighted_mean(x=x, *args, **kwargs)
        case 'geometric_mean' | 'gmean': return geometric_mean(x=x)
        case 'batch_geometric_mean' | 'batch_gmean': return batch_geometric_mean(x=x, *args, **kwargs)
        case 'harmonic_mean' | 'hmean': return harmonic_mean(x=x, *args, **kwargs)
        case 'batch_harmonic_mean' | 'batch_hmean': return batch_harmonic_mean(x=x, *args, **kwargs)
        case 'median': return median(x=x)
        case 'batch_median': return batch_median(x=x, *args, **kwargs)
        case 'mode': return mode(x=x)
        case 'batch_mode': return batch_mode(x=x, *args, **kwargs)
        case 'entropy': return entropy(x=x)
        case 'batch_entropy': return batch_entropy(x=x, *args, **kwargs)
        case 'variance' | 'var': return variance(x=x)
        case 'batch_variance' | 'batch_var': return batch_variance(x=x, *args, **kwargs)
        case 'std' | 'standard_deviation': return std(x=x)
        case 'batch_std' | 'batch_standard_deviation': return batch_std(x=x, *args, **kwargs)
        case 'skewness' | 'skew': return skewness(x=x)
        case 'batch_skewness' | 'batch_skew': return batch_skewness(x=x, *args, **kwargs)
        case _: raise ValueError(f'Unknown metric name: {metric_name}...')

Computes the mean of a 1D tensor.

Parameters:

Name Type Description Default
x Tensor

The input 1D tensor.

 required

Returns:

Type Description
Tensor

The mean value.
Source code in tinybig/koala/statistics/metric.py 
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
def mean(x: torch.Tensor):
    """
    Computes the mean of a 1D tensor.

    Parameters
    ----------
    x : torch.Tensor
        The input 1D tensor.

    Returns
    -------
    torch.Tensor
        The mean value.
    """
    assert x.ndim == 1
    return torch.mean(x)

Computes the mean along a specified dimension for a 2D tensor.

Parameters:

Name Type Description Default
x Tensor

The input 2D tensor.

 required
dim int

The dimension along which to compute the mean (0 or 1).

 1

Returns:

Type Description
Tensor

The mean values along the specified dimension.
Source code in tinybig/koala/statistics/metric.py 
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
def batch_mean(x: torch.Tensor, dim: int = 1):
    """
    Computes the mean along a specified dimension for a 2D tensor.

    Parameters
    ----------
    x : torch.Tensor
        The input 2D tensor.
    dim : int
        The dimension along which to compute the mean (0 or 1).

    Returns
    -------
    torch.Tensor
        The mean values along the specified dimension.
    """
    assert x.ndim == 2 and dim in [0, 1]
    return torch.mean(x, dim=dim)

Computes the geometric mean of a 1D tensor.

Parameters:

Name Type Description Default
x Tensor

The input 1D tensor. All elements must be positive.

 required

Returns:

Type Description
Tensor

The geometric mean value.
Source code in tinybig/koala/statistics/metric.py 
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
def geometric_mean(x: torch.Tensor):
    """
    Computes the geometric mean of a 1D tensor.

    Parameters
    ----------
    x : torch.Tensor
        The input 1D tensor. All elements must be positive.

    Returns
    -------
    torch.Tensor
        The geometric mean value.
    """
    assert x.ndim == 1 and torch.all(x > 0)
    log_x = torch.log(x)
    mean_log_x = torch.mean(log_x)
    return torch.exp(mean_log_x)

Computes the geometric mean along a specified dimension for a 2D tensor.

Parameters:

Name Type Description Default
x Tensor

The input 2D tensor. All elements must be positive.

 required
dim int

The dimension along which to compute the geometric mean (0 or 1).

 1

Returns:

Type Description
Tensor

The geometric mean values along the specified dimension.
Source code in tinybig/koala/statistics/metric.py 
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
def batch_geometric_mean(x: torch.Tensor, dim: int = 1):
    """
    Computes the geometric mean along a specified dimension for a 2D tensor.

    Parameters
    ----------
    x : torch.Tensor
        The input 2D tensor. All elements must be positive.
    dim : int
        The dimension along which to compute the geometric mean (0 or 1).

    Returns
    -------
    torch.Tensor
        The geometric mean values along the specified dimension.
    """
    assert x.ndim == 2 and dim in [0, 1] and torch.all(x > 0)

    log_x = torch.log(x)
    mean_log_x = torch.mean(log_x, dim=dim)
    return torch.exp(mean_log_x)

Computes the harmonic mean of a 1D tensor.

Parameters:

Name Type Description Default
x Tensor

The input 1D tensor. All elements must be positive.

 required
weights Tensor

The weights for each element in x.

 None

Returns:

Type Description
Tensor

The harmonic mean value.
Source code in tinybig/koala/statistics/metric.py 
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
def harmonic_mean(x: torch.Tensor, weights=None):
    """
    Computes the harmonic mean of a 1D tensor.

    Parameters
    ----------
    x : torch.Tensor
        The input 1D tensor. All elements must be positive.
    weights : torch.Tensor, optional
        The weights for each element in `x`.

    Returns
    -------
    torch.Tensor
        The harmonic mean value.
    """
    assert x.ndim == 1 and torch.all(x > 0)

    if weights is None:
        return x.numel() / torch.sum(1 / x)
    else:
        assert weights.ndim == 1 and x.shape == weights.shape
        weighted_sum = torch.sum(weights)
        weighted_reciprocal_sum = torch.sum(weights / x)
        return weighted_sum / weighted_reciprocal_sum

Computes the harmonic mean along a specified dimension for a 2D tensor.

Parameters:

Name Type Description Default
x Tensor

The input 2D tensor. All elements must be positive.

 required
weights Tensor

The weights for each element in the specified dimension.

 None
dim int

The dimension along which to compute the harmonic mean (0 or 1).

 1

Returns:

Type Description
Tensor

The harmonic mean values along the specified dimension.
Source code in tinybig/koala/statistics/metric.py 
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
def batch_harmonic_mean(x: torch.Tensor, weights=None, dim: int = 1):
    """
    Computes the harmonic mean along a specified dimension for a 2D tensor.

    Parameters
    ----------
    x : torch.Tensor
        The input 2D tensor. All elements must be positive.
    weights : torch.Tensor, optional
        The weights for each element in the specified dimension.
    dim : int
        The dimension along which to compute the harmonic mean (0 or 1).

    Returns
    -------
    torch.Tensor
        The harmonic mean values along the specified dimension.
    """
    assert x.ndim == 2 and dim in [0, 1] and torch.all(x > 0)

    if weights is not None:
        assert weights.ndim == 1 and x.shape[dim] == weights.shape[0]

    if weights is None:
        reciprocal_sum = torch.sum(1 / x, dim=dim)
        return x.shape[dim] / reciprocal_sum
    else:
        weighted_reciprocal_sum = torch.sum(weights / x, dim=dim)
        return torch.sum(weights, dim=dim) / weighted_reciprocal_sum

Computes the weighted mean of a 1D tensor.

Parameters:

Name Type Description Default
x Tensor

The input 1D tensor.

 required
weights Tensor

The weights for each element in x.

 required

Returns:

Type Description
Tensor

The weighted mean value.
Source code in tinybig/koala/statistics/metric.py 
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
def weighted_mean(x: torch.Tensor, weights: torch.Tensor):
    """
    Computes the weighted mean of a 1D tensor.

    Parameters
    ----------
    x : torch.Tensor
        The input 1D tensor.
    weights : torch.Tensor
        The weights for each element in `x`.

    Returns
    -------
    torch.Tensor
        The weighted mean value.
    """
    assert x.ndim == 1 and x.shape == weights.shape
    weighted_sum = torch.sum(x * weights)
    sum_weights = torch.sum(weights)
    return weighted_sum / sum_weights

Computes the weighted mean along a specified dimension for a 2D tensor.

Parameters:

Name Type Description Default
x Tensor

The input 2D tensor.

 required
weights Tensor

The weights for each element in the specified dimension.

 required
dim int

The dimension along which to compute the weighted mean (0 or 1).

 1

Returns:

Type Description
Tensor

The weighted mean values along the specified dimension.
Source code in tinybig/koala/statistics/metric.py 
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
def batch_weighted_mean(x: torch.Tensor, weights: torch.Tensor, dim: int = 1):
    """
    Computes the weighted mean along a specified dimension for a 2D tensor.

    Parameters
    ----------
    x : torch.Tensor
        The input 2D tensor.
    weights : torch.Tensor
        The weights for each element in the specified dimension.
    dim : int
        The dimension along which to compute the weighted mean (0 or 1).

    Returns
    -------
    torch.Tensor
        The weighted mean values along the specified dimension.
    """
    assert x.ndim == 2 and dim in [0, 1] and x.shape[1] == weights.shape[0]

    weights = weights.unsqueeze(0) if dim == 1 else weights.unsqueeze(1)
    weighted_sum = torch.sum(x * weights, dim=dim)
    sum_weights = torch.sum(weights, dim=dim)

    return weighted_sum / sum_weights

Computes the median of a 1D tensor.

Parameters:

Name Type Description Default
x Tensor

The input 1D tensor.

 required

Returns:

Type Description
Tensor

The median value.
Source code in tinybig/koala/statistics/metric.py 
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
def median(x: torch.Tensor):
    """
    Computes the median of a 1D tensor.

    Parameters
    ----------
    x : torch.Tensor
        The input 1D tensor.

    Returns
    -------
    torch.Tensor
        The median value.
    """
    assert x.ndim == 1
    return torch.median(x)

Computes the median along a specified dimension for a 2D tensor.

Parameters:

Name Type Description Default
x Tensor

The input 2D tensor.

 required
dim int

The dimension along which to compute the median (0 or 1).

 1

Returns:

Type Description
Tensor

The median values along the specified dimension.
Source code in tinybig/koala/statistics/metric.py 
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
def batch_median(x: torch.Tensor, dim: int = 1):
    """
    Computes the median along a specified dimension for a 2D tensor.

    Parameters
    ----------
    x : torch.Tensor
        The input 2D tensor.
    dim : int
        The dimension along which to compute the median (0 or 1).

    Returns
    -------
    torch.Tensor
        The median values along the specified dimension.
    """
    assert x.ndim == 2 and dim in [0, 1]
    return torch.median(x, dim=dim).values

Computes the mode of a 1D tensor.

Parameters:

Name Type Description Default
x Tensor

The input 1D tensor.

 required

Returns:

Type Description
Tensor

The mode value.
Source code in tinybig/koala/statistics/metric.py 
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
def mode(x: torch.Tensor):
    """
    Computes the mode of a 1D tensor.

    Parameters
    ----------
    x : torch.Tensor
        The input 1D tensor.

    Returns
    -------
    torch.Tensor
        The mode value.
    """
    assert x.ndim == 1
    return torch.mode(x)

Computes the mode along a specified dimension for a 2D tensor.

Parameters:

Name Type Description Default
x Tensor

The input 2D tensor.

 required
dim int

The dimension along which to compute the mode (0 or 1).

 1

Returns:

Type Description
Tensor

The mode values along the specified dimension.
Source code in tinybig/koala/statistics/metric.py 
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
def batch_mode(x: torch.Tensor, dim: int = 1):
    """
    Computes the mode along a specified dimension for a 2D tensor.

    Parameters
    ----------
    x : torch.Tensor
        The input 2D tensor.
    dim : int
        The dimension along which to compute the mode (0 or 1).

    Returns
    -------
    torch.Tensor
        The mode values along the specified dimension.
    """
    assert x.ndim == 2 and dim in [0, 1]
    return torch.mode(x, dim=dim)

Computes the standard deviation of a 1D tensor.

Parameters:

Name Type Description Default
x Tensor

The input 1D tensor.

 required

Returns:

Type Description
Tensor

The standard deviation value.
Source code in tinybig/koala/statistics/metric.py 
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
def std(x: torch.Tensor):
    """
    Computes the standard deviation of a 1D tensor.

    Parameters
    ----------
    x : torch.Tensor
        The input 1D tensor.

    Returns
    -------
    torch.Tensor
        The standard deviation value.
    """
    assert x.ndim == 1
    return torch.std(x)

Computes the standard deviation along a specified dimension for a 2D tensor.

Parameters:

Name Type Description Default
x Tensor

The input 2D tensor.

 required
dim int

The dimension along which to compute the standard deviation (0 or 1).

 1

Returns:

Type Description
Tensor

The standard deviation values along the specified dimension.
Source code in tinybig/koala/statistics/metric.py 
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
def batch_std(x: torch.Tensor, dim: int = 1):
    """
    Computes the standard deviation along a specified dimension for a 2D tensor.

    Parameters
    ----------
    x : torch.Tensor
        The input 2D tensor.
    dim : int
        The dimension along which to compute the standard deviation (0 or 1).

    Returns
    -------
    torch.Tensor
        The standard deviation values along the specified dimension.
    """
    assert x.ndim == 2 and dim in [0, 1]
    return torch.std(x, dim=dim)

Computes the entropy of a probability distribution represented by a 1D tensor.

Parameters:

Name Type Description Default
x Tensor

The input 1D tensor. Values must sum to 1.

 required

Returns:

Type Description
Tensor

The entropy value.
Source code in tinybig/koala/statistics/metric.py 
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
def entropy(x: torch.Tensor):
    """
    Computes the entropy of a probability distribution represented by a 1D tensor.

    Parameters
    ----------
    x : torch.Tensor
        The input 1D tensor. Values must sum to 1.

    Returns
    -------
    torch.Tensor
        The entropy value.
    """
    assert x.ndim == 1 and torch.all(x >= 0) and torch.isclose(torch.sum(x), torch.tensor(1.0)), "The tensor values must sum to 1."
    entropy_value = -torch.sum(x * torch.log(x + 1e-12))
    return entropy_value

Computes the entropy along a specified dimension for a 2D tensor.

Parameters:

Name Type Description Default
x Tensor

The input 2D tensor. Values in each dimension must sum to 1.

 required
dim int

The dimension along which to compute the entropy (0 or 1).

 1

Returns:

Type Description
Tensor

The entropy values along the specified dimension.
Source code in tinybig/koala/statistics/metric.py 
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
def batch_entropy(x: torch.Tensor, dim: int = 1):
    """
    Computes the entropy along a specified dimension for a 2D tensor.

    Parameters
    ----------
    x : torch.Tensor
        The input 2D tensor. Values in each dimension must sum to 1.
    dim : int
        The dimension along which to compute the entropy (0 or 1).

    Returns
    -------
    torch.Tensor
        The entropy values along the specified dimension.
    """
    assert x.ndim == 2 and dim in [0, 1]
    assert torch.all(x >= 0) and torch.allclose(torch.sum(x, dim=dim), torch.tensor(1.0))
    entropy_values = -torch.sum((x+1e-12) * torch.log(x), dim=dim)
    return entropy_values

Computes the variance of a 1D tensor.

Parameters:

Name Type Description Default
x Tensor

The input 1D tensor.

 required

Returns:

Type Description
Tensor

The variance value.
Source code in tinybig/koala/statistics/metric.py 
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
def variance(x: torch.Tensor):
    """
    Computes the variance of a 1D tensor.

    Parameters
    ----------
    x : torch.Tensor
        The input 1D tensor.

    Returns
    -------
    torch.Tensor
        The variance value.
    """
    assert x.ndim == 1
    return torch.var(x)

Computes the variance along a specified dimension for a 2D tensor.

Parameters:

Name Type Description Default
x Tensor

The input 2D tensor.

 required
dim int

The dimension along which to compute the variance (0 or 1).

 1

Returns:

Type Description
Tensor

The variance values along the specified dimension.
Source code in tinybig/koala/statistics/metric.py 
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
def batch_variance(x: torch.Tensor, dim: int = 1):
    """
    Computes the variance along a specified dimension for a 2D tensor.

    Parameters
    ----------
    x : torch.Tensor
        The input 2D tensor.
    dim : int
        The dimension along which to compute the variance (0 or 1).

    Returns
    -------
    torch.Tensor
        The variance values along the specified dimension.
    """
    assert x.ndim == 2 and dim in [0, 1]
    return torch.var(x, dim=dim)

Computes the skewness of a 1D tensor.

Parameters:

Name Type Description Default
x Tensor

The input 1D tensor.

 required

Returns:

Type Description
Tensor

The skewness value.
Source code in tinybig/koala/statistics/metric.py 
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
def skewness(x: torch.Tensor):
    """
    Computes the skewness of a 1D tensor.

    Parameters
    ----------
    x : torch.Tensor
        The input 1D tensor.

    Returns
    -------
    torch.Tensor
        The skewness value.
    """
    assert x.ndim == 1
    skewness_value = torch.mean((x - torch.mean(x)) ** 3) / (torch.std(x, unbiased=False) ** 3 + 1e-12)
    return skewness_value

Computes the skewness along a specified dimension for a 2D tensor.

Parameters:

Name Type Description Default
x Tensor

The input 2D tensor.

 required
dim int

The dimension along which to compute the skewness (0 or 1).

 1

Returns:

Type Description
Tensor

The skewness values along the specified dimension.
Source code in tinybig/koala/statistics/metric.py 
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
def batch_skewness(x: torch.Tensor, dim: int = 1):
    """
    Computes the skewness along a specified dimension for a 2D tensor.

    Parameters
    ----------
    x : torch.Tensor
        The input 2D tensor.
    dim : int
        The dimension along which to compute the skewness (0 or 1).

    Returns
    -------
    torch.Tensor
        The skewness values along the specified dimension.
    """
    assert x.ndim == 2 and dim in [0, 1]
    skewness_value = torch.mean((x - torch.mean(x, dim=dim, keepdim=True)) ** 3, dim=dim) / (torch.std(x, dim=dim, unbiased=False, keepdim=True) ** 3 + 1e-12)
    return skewness_value.squeeze(dim)