AI News, Hyperopt tutorial for Optimizing Neural Networks’ Hyperparameters

Hyperopt tutorial for Optimizing Neural Networks’ Hyperparameters

It is hence a good method for meta-optimizing a neural network which is itself an optimisation problem: tuning a neural network uses gradient descent methods, and tuning the hyperparameters needs to be done differently since gradient descent can’t apply.

Therefore, Hyperopt can be useful not only for tuning hyperparameters such as the learning rate, but also to tune more fancy parameters in a flexible way, such as changing the number of layers of certain types, or the number of neurons in a layer, or even the type of layer to use at a certain place in the network given an array of choices, each with nested tunable hyperparameters.

To sum up, it is more efficient to search randomly through values and to intelligently narrow the search space rather than looping on fixed sets of values for the hyperparameters.

parameter is defined with a certain uniformrange or else a probability distribution, such as: hp.randint(label, upper) hp.uniform(label, low, high) hp.loguniform(label, low, high) hp.normal(label, mu, sigma) hp.lognormal(label, mu, sigma) There is also a few quantized versions of those functions, which rounds the generated values at each step of “q”: hp.quniform(label, low, high, q) hp.qloguniform(label, low, high, q) hp.qnormal(label, mu, sigma, q) hp.qlognormal(label, mu, sigma, q) It is also possible to use a “choice” which can lead to hyperparameter nesting: hp.choice(label, ['list', 'of', 'potential', 'choices']) hp.choice(label, [hp.uniform(sub_label_1, low, high), hp.normal(sub_label_2, mu, sigma), None, 0, 1, 'anything']) Visualisations of the parameters for probability distributions can be found below.

plt.show() Note on the above charts (especially for the loguniform and uniform distributions): the blurred line averaging the values fades out toward the ends of the signal since it is zero-padded.

That’s because we want to observe changes in the learning rate according to changing it with multiplications rather than additions, e.g.: when adjusting the learning rate, we’ll want to try to divide it or multiply it by 2 rather than adding and substracting a finite value.

plt.show() Example – optimizing for finding the minimum of: f(x) = x^2 - x + 1 Let’s now define a simple search space and solve for f(x) = x^2 - x + 1, where x is an hyperparameter.

print('Found minimum after 1000 trials:') print(best) Found minimum after 1000 trials: {'x': 0.500084824485627} Example with a dict hyperparameter space Let’s solve for minimizing f(x, y) = x^2 + y^2 using a space using a python dict as structure.

print('Found minimum after 1000 trials:') print(best) Found minimum after 1000 trials: {'x': 0.013181950926553512, 'y': 0.0364742933684085} With choices, Hyperopt hyperspaces can be represented as nested data structures, too Yet, we have defined spaces as a single parameter.

hp.normal('a', 0, 2), hp.uniform('b', 0, 3), hp.choice('c', [False, True]),

'yet_another_dict_recursive': {'u': -2.0565596833626976, 'v': 1.0738132202239536}} Let’s now record the history of every trial This will require us to import a few more things, and return the results with a dict that has a “status” and “loss” key at least.

print('What interests us most is the 'result' key of each trial (here, we show 7):') pp.pprint(trials.trials[0]['result']) pp.pprint(trials.trials[1]['result']) pp.pprint(trials.trials[2]['result']) pp.pprint(trials.trials[3]['result']) pp.pprint(trials.trials[4]['result']) pp.pprint(trials.trials[5]['result']) pp.pprint(trials.trials[6]['result']) #

'idxs': {'x': [0], 'y': [0]},

'tid': 0,

'vals': { 'x': [-0.2682564852440139],

'y': [-3.6433914388359234]},

'workdir': None},

'space': {'x': -0.2682564852440139, 'y': -3.6433914388359234},

'status': 'ok'},

'idxs': {'x': [1], 'y': [1]},

'tid': 1,

'vals': {'x': [1.1193079488707536], 'y': [4.941591090140912]},

'workdir': None},

'space': {'x': 1.1193079488707536, 'y': 4.941591090140912},

'status': 'fail'},

'idxs': {'x': [2], 'y': [2]},

'tid': 2,

'vals': {'x': [-0.9841176113491965], 'y': [4.084615269991156]},

'workdir': None},

'space': {'x': -0.9841176113491965, 'y': 4.084615269991156},

'status': 'fail'},

'status': 'fail'} Up next: saving results to disk while optimizing for resuming a stopped hyperparameter search Note that the optimization could be parallelized by using MongoDB and storing the trials’ state here.

hoomd.comm¶

hoomd.comm.barrier Perform a MPI barrier synchronization across all ranks in the partition.

hoomd.comm.barrier_all Perform a MPI barrier synchronization across the whole MPI run.

background-repeat

By default, the repeated images are clipped to the size of the element, but they can be scaled to fit (using round) or evenly distributed from end to end (using space).

Inherited no Media visual Computed value a list, each item consisting of two keywords, one per dimension Animation type discrete Canonical order the unique non-ambiguous order defined by the formal grammar Syntax Values <repeat-style> The one-value syntax is a shorthand for the full two-value syntax: Single value Two-value equivalent repeat-x repeat no-repeat repeat-y no-repeat repeat repeat repeat repeat space space space round round round no-repeat no-repeat no-repeat In the two-value syntax, the first value represents the horizontal repetition behavior and the second value represents the vertical behavior.

round As the allowed space increases in size, the repeated images will stretch (leaving no gaps) until there is room (space left >= half of the image width) for another one to be added.

Candidate Recommendation Adds support for multiple background images, the two-value syntax allowing distinct repetition behavior for the horizontal and vertical directions, the space and round keywords, and for backgrounds on inline-level elements by precisely defining the background painting area.

Browser compatibility Desktop Mobile Feature Chrome Edge Firefox Internet Explorer Opera Safari Basic support 1 12 1 4 3.5 1 Multiple backgrounds 1 12 3.6 9 10.5 1.3 Two-value syntax (different values for x & y directions) Yes 12 13 9 Yes Yes round and space keywords Yes 12 49 9 10.5 Yes See also Using multiple backgrounds Document Tags and Contributors Tags: CSS CSS Background CSS Property Reference

Contributors to this page: mfluehr, fscholz, Arty-chan, xfq, dyf19118, teoli, erikadoyle, Sebastianz, yisibl, SphinxKnight, MarkusStange, wbamberg, jsx, chrisAnderson, TWebs, Sheneman, J-Mackerel, kscarfone, Sheppy, ethertank, tregagnon, leaverou, estelle, grendel, JonRimmer, Alex Lakatos, Mgjbot, BijuGC, Gabrys, Qazzian, Sembiance, alecananian, Readams </repeat-style>

Hausdorff space

^ Willard, pp.

See for instance Lp space#Lp spaces, Banach–Mazur compactum etc.

'An anti-Hausdorff Fréchet space in which convergent sequences have unique limits'.

'Proof of A compact set in a Hausdorff space is closed'.

Float Extension

By implementing the advanced float features, AH Formatter V6.2 is capable of arranging the float content in an arbitrary place of the page, arranging the float content in multi-column layout with column spanning of the float.

background-repeat

If a background-image property is specified, the background-repeat property in CSS defines if (and how) it will repeat.

These are the possible values for this property (besides the usual stuff like inherit): repeat: tile the image in both directions.

repeat-x: tile the image horizontally repeat-y: tile the image vertically no-repeat: don't tile, just show the image once space: tile the image in both directions.

Browser Support Chrome Safari Firefox Opera IE Android iOS 1+ 1+ 1+ 3.5+ 4+ 1+ 1+ The comma-separated multiple value synta only supported in Firefox 3.6+ and IE 9+.

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