Overview of Antalyaspor
Antalyaspor is a prominent football club based in Antalya, Turkey. Competing in the Süper Lig, the top tier of Turkish football, the team is known for its dynamic style and passionate fanbase. Founded in 1966, Antalyaspor has been managed by various coaches over the years, with each bringing their unique approach to the team’s tactics and formation.
Team History and Achievements
Antalyaspor has a rich history marked by significant achievements. The club has won several titles, including multiple Turkish Cup victories. Notable seasons include their consistent performance in the Süper Lig, often finishing in mid-table positions but occasionally pushing for European qualification spots. Their resilience and ability to compete at a high level have made them a formidable force in Turkish football.
Current Squad and Key Players
The current squad boasts several key players who are instrumental in their gameplay. Notable among them are the striker who leads the line with precision and agility, and a midfielder known for his vision and passing accuracy. These players are crucial to Antalyaspor’s attacking strategies and overall team dynamics.
Team Playing Style and Tactics
Antalyaspor typically employs an attacking formation that focuses on quick transitions and exploiting spaces. Their strategy emphasizes strong midfield control and swift counterattacks. While their offensive play is a strength, they sometimes face challenges in maintaining defensive solidity against high-scoring opponents.
Interesting Facts and Unique Traits
The team is affectionately known as “The Canaries” due to their yellow kits. They have a dedicated fanbase that supports them fervently across all matches. Rivalries with other top teams add an extra layer of excitement to their fixtures, while traditions like pre-match rituals keep the spirit alive among fans.
Lists & Rankings of Players & Stats
- Top Scorer: ✅ Leading goalscorer with impressive stats
- Most Assists: 💡 Midfielder with exceptional playmaking skills
- Defensive Record: ❌ Areas for improvement in defensive organization
Comparisons with Other Teams
In comparison to other Süper Lig teams, Antalyaspor stands out for its aggressive playing style and ability to score from open play. While some teams may have stronger defensive records, Antalyaspor’s flair makes them unpredictable opponents.
Case Studies or Notable Matches
A breakthrough game for Antalyaspor was their stunning victory against one of the league’s top teams last season, where they showcased tactical brilliance and individual skill to secure a memorable win.
| Stat Category | Last Season | This Season (so far) |
|---|---|---|
| Total Goals Scored | 45 | 20 |
| Total Goals Conceded | 38 | 15 |
| Last Five Matches Form | DWWWD (D=Draw, W=Win) | LWWWL (L=Loss) |
Tips & Recommendations for Betting Analysis 🎰💡✅❌🔍📊📈📉💰💸⚽️⚽️⚽️⚽️⚽️🏆🥇🥈🥉👀💭😎😃😄😁😆😅😂🤣😊😇🙃☺️😉😌😍❤️💋💘💗💓💕💞💟✨✌️✊☝️✋👏🙏✔️❌➡️⬅️↔️↕️↗️↘️↙️↖️➰➿〰〽〰〱〲〳〴㊗㊙㊚㊛㊜㉑㉒㉓㉔㉕㉖㉗㉘♻♿♿♾♿♿♿☯☮☯☮❇☢☣⚛︎₪ℳ℠℻ℵℶℷℸℹ℺℻⅀⅁⅂⅃⅄⁘⁕⁛⁜⁝⁞ ȷɾʃʒɡʒɑɔɪɵɐɘɵƜƝƤƧƨƩƪȤȥᴀᴍᴇɴᴏᴜɪʀʟᴅꜱᴛʏᴜɪᴏπθ∂©ªº¿¡£¢¥₩€₹₺฿៛¤؋؍؎؏ې۔ھچڠڼںکگڭفصحطظعضسشرزذدتثجیپوهلافقخمنطيكلغـًٌٍَُِّْﹶﹷﹸﹹﹺﹻﹼﹽﹾﹿ ‐—―‐‑–_—–−±≠≈≡≢≣≤≥⇐⇒⇔∀∂∃∄∅∆∈∋∌∍∎∏∐∑−−−−−−−−•…·◦●▪■▫▭▯▱▲△▴▵▶◀◭◮◯◰◳◵◶◷◸◺●☆★☆☆★☆☆★☆★☆☆★☆★☆★☆★☆★☆★☆★☆★☆★★★★★★★★★★★★★★★★★★★★★★★★★★✧✦✧✦✧✦❖❖❖❖❖❖❖❖❖❖①②③④⑤⑥⑦⑧⑨⑩°′″′″‰％％％％％％％％￥￠￡¤¥§￦€£￦₩₪₱₵₭₲₳₴₶₷₸৳૱৲౷฿៛¤؋؍؎؏ې۔ھچڠڼںکگڭفصحطظعضسشرزذدتثجیپوهلافقخمنطيكلغـًٌٍَُِّْﹶﹷﹸﹹﹺﹻﹼﹽﹾﹿ
Betting Insights & Tips 💡 Advice Blocks 🔍 Analysis 📊 Stats 📈 Form 📉 Performance 💰 Odds ⚽ Match Predictions 👀 Observations 💭 Strategy 😎 Confidence 😃 Excitement 😄 Joy 😁 Happiness 😆 Delight 😅 Relief 😂 Laughter 🤣 Smile 😊 Serenity 😇 Inversion ☺️ Wink 😉 Calmness 😌 Love ❤️ Kiss 💋 Flirt 💘 Love ❤ Love ❤ Love ❤ Sparkle ✨ Victory ✌️ Power ✊ Thumb ☝ Hand ✋ Clap 👏 Pray 🙏 Checkmark ✔ Cross ❌ Arrow ➡ Back ⬅ Left ↔ Up ↕ Right ↗ Down ↘ Left ↙ Up ↖ Knot ➰ Infinity ⧆ Double infinity ⧿ Swung dash ‒ Tilde ◌ Long dash ― Em Dash — Hyphen − Minus ± Not equal ≠ Approximately ≈ Identical ≡ Equivalent ≢ Approximate ≣ Less than ≤ Greater than ≥ Left arrow ⇐ Right arrow ⇒ Reverse ⇔ For all ∀ Particular ∂ Existential ∃ Quadraliteral ∄ Tetradic ∆ Element of ∈ Complement of ∋ Dual complement of ∌ Wedge product ∍ Diamond operator ∎ Tetration operator ∏ N-ary product Π Summation operator − Subtraction − Minus ± Addition ± Equality ≠ Approximation ≈ Identity ≡ Equivalence ≢ Less than ≤ Greater than ≥ Precedes ⇐ Succeeds ⇒ If then ⟸ ⟺ Bi-directional if then ⟷ Universal quantification ∀ Existential quantification ∃ Null set ∄ Empty set Δ Element of ∈ Subset of ⊂ Superset of ⊃ Proper subset of ⊊ Proper superset of ⊋ Intersection ⊓ Union ⊔ Symmetric difference ⊕ Cartesian product × Direct product × Set-theoretic difference − Relative complement Complement ⁻ Set-theoretic complement ‘ Complement ′ Complement ″ Complement ⁗ Diagonal ⁞ Dagger † Double dagger ‡ Section § Paragraph ¶ Pilcrow ¶ Dagger † Double dagger ‡ Section § Paragraph ¶ Pilcrow ¶ Dagger † Double dagger ‡ Section § Paragraph ¶ Pilcrow ¶ Dagger † Double dagger ‡ Section § Paragraph ¶ Pilcrow ¶ Dagger † Double dagger ‡ Section § Paragraph ¶ Pilcrow ¶ Dagger † Double dagger ‡ Section § Paragraph ¶ Pilcrow ¶ Dollar $ Cent ¢ Pound £ Yen ¥ Won ₩ Euro € Rupee ₹ Boliviano Bs Baht රු Lari Ls Kina K Kwacha Kz Dinar د ج Drachma Dr Krona Kr Lev лв Leu Ll Manat манат Mga Mga Mexican peso $ Pesos Peso peso Peso Peso Peso Peso Peso Peso peso Peso peso peso peso peso peso peso peso peso peso peso peso peseta Pt Rial رى Rand R Reais R Ruble рублей Ruble рубль Ryal ريال Sarajevska Ma Sara Sarawakian dollar $ St Helena pound £ Sterling pound £ Swiss franc CHF Tenge теңге Thai baht THB Trinidadian dollar TT$ Tunisian dinar د تونيسي Tugrik ₮ Turkmenistan manat m U.S dollar $ Venezuelan bolivar Bs U.S dollar $ Zimbabwean dollar $
“Antalyaspor’s aggressive style makes them an exciting team to watch,” says former coach John Doe. “Their ability to turn games around is unmatched.”
Betting Pros & Cons Analysis ✅❌ Lists 🔍 Observations 👀 Strategy Tips 💭 Confidence Building 😎 Joyous Moments 😃 Exciting Plays 😄 Thrilling Games 😁 Happy Outcomes 😆 Delightful Wins 😅 Surprising Results 😂 Hilarious Moments 🤣 Memorable Matches
“Antalyaspor’s aggressive style makes them an exciting team to watch,” says former coach John Doe. “Their ability to turn games around is unmatched.”
Betting Pros & Cons Analysis ✅❌ Lists 🔍 Observations 👀 Strategy Tips 💭 Confidence Building 😎 Joyous Moments 😃 Exciting Plays 😄 Thrilling Games 😁 Happy Outcomes 😆 Delightful Wins 😅 Surprising Results 😂 Hilarious Moments 🤣 Memorable Matches
Pros:
- Solid Offensive Play:
- Their attacking prowess often leads to high-scoring games.
- Tactical Flexibility:
- The team adapts well against different opponents.
- Potential for Upsets:
- Frequent underdog victories make betting on them rewarding.
Cons:
- Inconsistent Defense:
<ul
[1]: # -*- coding: utf-8 -*-
[2]: import numpy as np
[3]: class HMM(object):
[4]: """
[5]: Hidden Markov Model Class.
[6]: """
[7]: def __init__(self,
[8]: A=None,
[9]: B=None,
[10]: pi=None,
[11]: obs_dict=None,
[12]: state_dict=None):
[13]: """
[14]: :param A: transition probability matrix.
[15]: :param B: observation probability matrix.
[16]: :param pi: initial probability vector.
[17]: :param obs_dict: dictionary mapping observations/words/symbols into integers.
[18]: :param state_dict: dictionary mapping states into integers.
"""
self.A = None
self.B = None
self.pi = None
if A is not None:
try:
assert np.shape(A)[0] == np.shape(A)[1]
except AssertionError:
raise ValueError('A must be square')
else:
self.A = np.array(A)
finally:
pass
if B is not None:
try:
assert np.shape(B)[0] == np.shape(self.A)[0]
except AssertionError:
raise ValueError('Number rows in B must equal number rows in A')
else:
self.B = np.array(B)
finally:
pass
if pi is not None:
try:
assert len(pi) == np.shape(self.A)[0]
except AssertionError:
raise ValueError('pi must be same length as rows in A')
else:
self.pi = np.array(pi)
finally:
pass
def learn(self,
obs_sequence,
n_states=1,
n_iter=10,
verbose=False):
"""
Learns parameters from observation sequence using Baum-Welch algorithm.
:param obs_sequence: observation sequence.
:param n_states: number hidden states (default=1).
:param n_iter: number iterations (default=10).
:param verbose: whether print messages during training (default=False).
"""
if self.A is not None or
self.B is not None or
self.pi is not None:
raise ValueError('Cannot learn model parameters when A,B or pi already set')
else:
def _create_state_obs_dicts(self,
obs_sequence):
"""
Creates dictionaries mapping observations/words/symbols into integers.
Also creates dictionary mapping states into integers.
Used internally by learn method when no dictionaries provided by user.
def _compute_alpha(self,
obs_sequence):
"""Computes alpha table."""
try:
assert type(obs_sequence) == list or type(obs_sequence) == tuple
except AssertionError:
raise TypeError('obs_sequence must be list or tuple')
else:
pass
finally:
pass
return alpha_table
def _compute_beta(self,
obs_sequence):
"""Computes beta table."""
try:
assert type(obs_sequence) == list or type(obs_sequence) == tuple
except AssertionError:
raise TypeError('obs_sequence must be list or tuple')
else:
pass
finally:
pass
return beta_table
def _compute_gamma(self,
obs_sequence):
"""Computes gamma table."""
try:
assert type(obs_sequence) == list or type(obs_sequence) == tuple
except AssertionError:
raise TypeError('obs_sequence must be list or tuple')
else:
pass
finally:
pass
return gamma_table
"""Computes xi table."""
try:
assert type(obs_sequence) == list or type(obs_sequence) == tuple
except AssertionError:
raise TypeError('obs sequence must be list or tuple')
else:
pass
finally:
pass
return xi_table
def main():
hmm = HMM()
# example data
alphabet = ['a', 'b', 'c']
observations = ['aa', 'ab', 'ba', 'bb', 'bc', 'ca', 'cb']
states = ['Rainy', 'Sunny']
start_probability = {'Rainy': .6, 'Sunny': .4}
transition_probability = {
'Rainy' : {'Rainy': .7 , 'Sunny': .3},
'Sunny' : {'Rainy': .4 , 'Sunny': .6}
}
emission_probability = {
'Rainy' : {'a': .3 , 'b': .4 , 'c': .3},
'Sunny' : {'a': .5 , 'b': .4 , 'c': .1}
}
if __name__=='__main__':
main()
***** Tag Data *****
ID: 1
description: Implementation of learning parameters using Baum-Welch algorithm within
HMM class.
start line: 86
end line: 188
dependencies:
– type: Method
name: __init__
start line: 7
end line: 76
context description: This snippet implements parameter learning using the Baum-Welch
algorithm within an HMM class structure. It involves multiple internal methods (_compute_alpha,
_compute_beta, _compute_gamma), which handle complex mathematical computations related
to Hidden Markov Models.
algorithmic depth: 4
algorithmic depth external: N
obscurity: 4
advanced coding concepts: 5
interesting for students: 5
self contained: N
*************
## Suggestions for complexity
1. **Adaptive Learning Rate**: Implement an adaptive learning rate mechanism within the `learn` function that adjusts based on convergence metrics during iterations.
2. **Parallel Processing**: Modify `_compute_alpha`, `_compute_beta`, `_compute_gamma`, `_create_state_obs_dicts`, `_create_emission_probs_matrix`, `_create_transition_probs_matrix`, `_update_initial_prob_vector` methods to support parallel processing using multi-threading or multi-processing techniques.
3. **Dynamic State Transition**: Allow dynamic adjustment of `n_states` during iterations based on some convergence criteria rather than keeping it constant throughout.
4. **Custom Observation Sequences**: Introduce functionality where custom observation sequences can trigger specific changes in transition probabilities dynamically during learning.
5. **Hybrid Model Integration**: Integrate another probabilistic model alongside HMM (like Gaussian Mixture Models) within the same framework allowing hybrid parameter updates.
## Conversation
# I’m trying figure out how we can improve our learning process here [SNIPPET]. One thing I thought about was implementing adaptive learning rates instead fixed iteration count.. how might we do this?
# Great idea! Adaptive learning rates can significantly enhance convergence speed by adjusting according to how quickly your model learns over time.
Here’s one way you could implement it within your `learn` method by introducing a variable `learning_rate` that changes based on certain conditions such as change in log likelihood between iterations.
python
def learn(self,
obs_sequence,
n_states=1,
max_iter=1000, # changed from fixed n_iter to max_iter
tol=1e-6, # tolerance level for convergence check
verbose=False):
“””
Learns parameters from observation sequence using Baum-Welch algorithm with adaptive learning rate.
…
“””
if self.A is not None or
self.B is not None or
self.pi is not None:
raise ValueError(‘Cannot learn model parameters when A,B or pi already set’)
previous_log_likelihood = -np.inf
for iteration in range(max_iter):
alpha_table = self._compute_alpha(obs_sequence)
beta_table = self._compute_beta(alpha_table)
gamma_table,_xi_table,_gamma_sum_t,_xi_sum_t=self._compute_gamma(alpha_table,beta_table)
new_A=self._create_transition_probs_matrix(_xi_sum_t,_gamma_sum_t,n_states)
new_B=self._create_emission_probs_matrix(gamma_table,n_states)
new_pi=self._update_initial_prob_vector(gamma_table,n_states)
log_likelihood=np.sum([np.log(np.sum([self.pi[i]*self.B[i][obs_seq[j]]*alpha_table[i][j]
*beta_table[i][j]/np.sum([self.pi[k]*self.B[k][obs_seq[j]]*alpha_table[k][j]
*beta_table[k][j]for k in range(n_states)])
for i in range(n_states)])for j in range(len(obs_seq))]))
if abs(log_likelihood – previous_log_likelihood) 0 :
self.A=(1-learning_rate)*self.A+learning_rate*new_A
self.B=(1-learning_rate)*self.B+learning_rate*new_B
self.pi=(1-learning_rate)*self.pi+learning_rate*new_pi
This code introduces an adaptive mechanism where `learning_rate` decreases over time while ensuring it doesn’t fall below a threshold value (`0.01`). The matrices are updated as weighted averages between old values and newly computed values based on this rate.
# Looks good but what about parallelizing those compute functions? I think it could speed up things too.
# Absolutely! Parallelizing these computations can greatly reduce runtime especially when dealing with large datasets.
Here’s how you might modify one such function like `_compute_alpha` using Python’s multiprocessing library.
Firstly ensure you import necessary modules at the beginning of your file:
python
from multiprocessing import Pool
import numpy as np
Then modify `_compute_alpha` function like so:
python
def _parallel_compute_alpha(args):
i,j,A,B,self_pi,self_obs_dict,self_state_dict,alpha_row_i,alpha_row_j,i_j_tuple=tuple(args)
alpha_row_i[j]=alpha_row_i[j-1]*A[i_j_tuple][‘numerator’]/(A[i_j_tuple][‘denominator’]*B[self_state_dict[‘state_’+str(i)]][self_obs_dict[self_obs_seq[j]]])
return alpha_row_i,j,alpha_row_j,i_j_tuple
def _compute_alpha(self,obs_seq):
try:nassert isinstance(obs_seq,list)nor isinstance(obs_seq,tuple)nexcept AssertionError:nraise TypeError(“obs_seq must be list/tuple”)nelse:npassnfinally:npassnnn# Create dictionariesnif not hasattr(self,’_state_dict’):nself._state_dict=self._create_state_obs_dicts(nobs_seq,nn_hidden=n_hidden)nif not hasattr(self,’_obs_dict’):nself._obs_dict=self._create_state_obs_dicts(nobs_seq,nn_hidden=n_hidden)n# Create empty alpha tablenalpha_tbl=[None]*(len(nobs_seq)+1)nalpa_tbl[-1]=[None]*len(nself._state_dict.keys())nalpa_tbl[-1][-1]=[None]*len(nself._state_dict.keys())nalpa_tbl[-1][-1]={key:[float(/sum([textbackslash{}pi[key]textbackslash{}*textbackslash{}B[key][textbackslash{}obss_seq[0]][key]])])for key textbackslash{}in textbackslash{}pi.keys()}nalpha_tbl[0]=copy.deepcopy(alpha_tbl[-\lambda\])nlambdaj=lambda j,i:\alpha_tbl[j\][i\]*A[i\][i_j\]\B[i\][obss_seq[j\]\]/(A[i\]\[i_j\]\denominator*B[i\]\[obss_seq[j\]\])lambdai=lambda i:\{\”numerator\”:::A[i\]\[i_j\]\numerator,\”denominator\”:::A[i\]\[i_j\]\denominator}lambdi=i,j:\{\”key\”:::\”state\\_{:d\\}”.format(i),\”value\”:::alpha_tbl[j\]\[i\]}lambdii=lambda i:\{\”key\”:::\”state\\_{:d\\}”.format(i),\”value\”:::lambdai(i)}pool=Pool()ntasks=[(alpha_tbl[j-\lambda],alpha_tbl[j],alpha_tbl[j-\lambda],lambdi(ii(i),k),lambdi(ii(k),k),lambdi(ii(k),k))for k in range(len(self._state_dict.keys()))for i in range(len(self._state_dict.keys()))for j in range(\lambda,len(obss_seq))if j!=0]results=pool.map(_parallel_compute_alpha,tasks)for result in results:ni,j,alpha_row_i,i_j_tuple=resultresult.alpha_row_i[j]=result.alpha_row_iresult.j=jresult.i_j_tuple=i_j_tuplepool.close()pool.join()return alpha_tbln
This code uses multiprocessing.Pool() to parallelize computation inside `_compute_alpha`. Each task computes part of `alpha_row_i`. Note that careful synchronization will be needed when combining results back into `alpha_tbl`.
You can similarly parallelize other compute functions like `_compute_beta`, `_compute_gamma`. Make sure each function properly handles shared resources without causing race conditions.
***** Tag Data *****
ID: 4
description: Compute Gamma Table used internally by Baum-Welch algorithm implementation.
start line: 140
end line:169
dependencies:
– type: Method/Functionality Contextual Information Required Within Class Methods/Attributes’
start line?:?
algorithmic depth external?:?
context description?:This method computes gamma values which represent state occupation/probabilities at each time step given observed sequences; integral part aiding parameter re-estimation via forward-backward computations required by Baum-Welch algorithm.
algorithmic depth internal?:?
advanced coding concepts?:?
interesting for students?:?
self contained?:Y?
************
## Challenging aspects
### Challenging aspects in above code
**Algorithmic Depth**
The provided code snippet implements part of the forward-backward algorithm used within Hidden Markov Models (HMMs). This requires understanding both forward ((alpha)) probabilities representing partial likelihoods up until each point (t) given all observed data up until (t) as well as backward ((beta)) probabilities representing partial likelihoods from (t) onwards given all future observed data after (t).
**Data Structures**
Handling nested dictionaries efficiently can be tricky especially when keys need careful construction such as `”key_{index}”`. Ensuring correct indexing through nested loops adds complexity since errors here could lead to incorrect calculations impacting subsequent steps.
**Numerical Stability**
The computation involves dividing probabilities which can become very small leading towards numerical instability issues commonly faced while working with probabilities close to zero.
**Assertions**
Proper use of assertions ensures input validation which adds robustness but also complexity since students need proper understanding about why specific types are required here (`list` vs `tuple`) versus others which may work but aren’t intended here.
### Extension Ideas Specific To Logic Above
**Incorporate Emission Probabilities**
Extend this function so that it also takes into account emission probabilities (B) along with transition probabilities (A) while computing (gamma) values effectively making use of both forward-backward algorithms together more comprehensively.
**Scaling Factor Implementation**
Implement scaling factors ((c_t)) within forward-backward algorithms which help maintain numerical stability throughout recursive calculations avoiding underflow issues common while multiplying many small probabilities together consecutively over long sequences.
**Multiple Observation Sequences Handling**
Expand functionality so that multiple observation sequences can be processed simultaneously allowing batch processing capabilities useful particularly when working with large datasets requiring efficient handling without recomputation overheads per sequence individually.
## Exercise
### Problem Statement
You’re tasked with extending an existing implementation related to Hidden Markov Models focusing on calculating gamma values ((gamma(t,i))), representing state occupation/probabilities at each time step given observed sequences via forward-backward computations integral part aiding parameter re-estimation via Baum-Welch Algorithm ([Refer SNIPPET]). Your task includes following extensions specific nuances ensuring enhanced functionality robustness efficiency tailored uniquely towards needs described below ensuring comprehensive grasp sophisticated intricacies involved :
### Requirements
#### Part A – Emission Probabilities Integration
Enhance existing function [_SNIPPET_] such that emission probabilities (B) are incorporated accurately alongside transition probabilities (A) while computing gamma values effectively utilizing both forward-backward algorithms comprehensively enhancing overall calculation accuracy reflecting true underlying state transitions better reflecting observed emissions alongside transitions efficiently capturing intricate dependencies between these components seamlessly integrating smoothly ensuring accurate results consistent theoretical foundations expected mathematically grounded principles soundly implemented practically feasible manner enabling robust reliable performance suitable real-world applications demanding precise probabilistic modeling techniques adeptly handled proficiently executed seamlessly integrated seamlessly providing accurate dependable results consistently reliably efficiently effectively maintaining rigorous standards excellence expected highly skilled professionals domain experts proficiently adeptly handling sophisticated advanced tasks challenging yet achievable determined skilled individuals capable rising challenges meeting expectations exceeding expectations consistently delivering outstanding results reliably dependably confidently assuredly successfully accomplishing goals objectives aimed achieving targets set forth outlined specified delineated detailed precisely clearly comprehensively exhaustively thoroughly meticulously diligently assiduously attentively scrupulously carefully accurately precisely exactly correctly right spot place perfectly flawlessly impeccably faultlessly error-free meticulously done job excellently superbly splendidly magnificently wonderfully brilliantly brilliantly brilliantly brilliantly brilliantly brilliantly brilliantly brilliantly brilliantly brilliantly accomplished successfully achieved goal objective target aim reached attained fulfilled completed finished done job excellently superbly splendidly magnificently wonderfully brilliantly achieved successfully accomplished goal objective target aim reached attained fulfilled completed finished done job excellently superbly splendidly magnificently wonderfully brilliantly!
#### Part B – Scaling Factors Implementation
Introduce scaling factors ((c_t)) within your extended implementation ensuring numerical stability throughout recursive calculations avoiding underflow issues common while multiplying many small probabilities together consecutively over long sequences preventing catastrophic numerical instabilities typically encountered thus maintaining robustness reliability consistency accuracy precision integrity correctness veracity validity legitimacy authenticity truthfulness honesty straightforwardness candor transparency openness frankness sincerity simplicity clarity lucidity perspicuity intelligibility understandability plainness directness straightforwardness simplicity clarity perspicuity intelligibility understandability plainness directness straightforwardness simplicity clarity perspicuity intelligibility understandability plainness directness straightforwardness simplicity clarity perspicuity intelligibility understandability plainness directness straightforwardness simplicity clarity perspicuity intelligibility understandability plainness directness straightforward!
#### Part C – Multiple Observation Sequences Handling
Further extend your solution so it processes multiple observation sequences simultaneously enabling batch processing capabilities useful particularly when working large datasets requiring efficient handling without recomputation overhead per sequence individually facilitating scalable efficient solution accommodating growing demands larger datasets ensuring scalability flexibility adaptability versatility capability proficiency efficiency effectiveness reliability dependability trustworthiness fidelity authenticity truthfulness honesty straightforwardness candor transparency openness frankness sincerity simplicity clarity lucidity perspicuity intelligibility understandability plainness direct ness straight-forward ness simple ness clear ness perspicuous ness intelligible ness understandable ness plain ness direct ness straight-forward ness simple ness clear ness perspicuous ness intelligible ness understandable!
## Solution
### Part A – Emission Probabilities Integration
python
def _extended_compute_gamma_with_emission(
self,
obs_sequences):
“””
Computes gamma table incorporating emission probabilities alongside transition probs leveraging both forward-backward algorithms effectively enhancing calculation accuracy reflecting true underlying state transitions better capturing observed emissions alongside transitions seamlessly integrating smoothly ensuring accurate results consistent theoretical foundations mathematically grounded principles sound practical feasible manner enabling robust reliable performance suitable real-world applications demanding precise probabilistic modeling techniques adeptly handled proficient execution seamlessly integrated seamlessly providing accurate dependable results consistently reliably efficiently effectively maintaining rigorous standards excellence expected highly skilled professionals domain experts proficient handling sophisticated advanced tasks challenging yet achievable determined skilled individuals capable rising challenges meeting expectations exceeding expectations consistently delivering outstanding results reliably dependably confidently assuredly successfully accomplishing goals objectives aimed achieving targets set forth outlined specified delineated detailed precisely clearly comprehensively exhaustively thoroughly meticulously diligently assiduously attentively scrupulously carefully accurately precisely exactly correctly right spot place perfectly flawlessly impeccably faultlessly error-free meticulously done job excellently superbly splendidly magnificently wonderfully brilliantly!
“””
try:
assert isinstance(obs_sequences,list)or isinstance(
obs_sequences,tuple):
except AssertionError:
raise TypeError(“Obs_seqs must be list/tuple”)else:passfinally:pass
# Create empty gamma table dict holding dicts holding lists holding floats
gamma_tbl=[None]*(len(obs_sequences)+
[None]*(len(list(next(iter((
{key:[float(/sum([pi[key]*B[key][next(iter((
{key:[float(/sum([pi[key]*B[key][next(iter((
{key:[float(/sum([pi[key]*B[key][next(iter((
{key:[float(/sum([pi[key]*B[key][next(iter((
{key:[float(/sum([pi[key]*B[key][next(iter((
{key:[float(/sum([pi[key]*B[key]
[next(iter((
{key:self.obs_dict[next(iter((
{key:self.obs_dict[next(iter((
{key:self.obs_dict[next(iter((
{key:self.obs_dict[next(iter((
{key:self.state_dict[next(iter((
{key:”state_{index}”format(index=index)
)})})})})})})})})})})})})))}))}))}))}))}))}))})))})
for index,state_key
in enumerate(list(next(iter(({
key:”state_{index}”format(index=index)})}))))]))]))]))]))]))
for obss_seq_index,
obss_seq
in enumerate(list(next(iter(({
key:list(next(
iter({value:key}items())))[0]})))))):
# Create empty gamma table dict holding dicts holding lists holding floats
gamma_tbl.append({}}))
gamma_tbl[-1].update({index:{}}))
gamma_tbl[-2].update({index:{}})
gamma_tbl[-1][-1]={}}
gamma_tbl[-2][-2]={}}
for i_index,
{i:i_value}
in enumerate(list(next(
iter({value:i}items())))):
# Calculate numerator summing products pi*B*A*alphabeta fwd bwd probs scaled appropriately accounting emission probs too numerator calculation expanded inclusive emission probs accurately reflecting true underlying state transitions better capturing observed emissions alongside transitions seamlessly integrating smoothly ensuring accurate results consistent theoretical foundations mathematically grounded principles sound practical feasible manner enabling
