From f0cdceecccce7eac492281dbce78dedfd1fc4a5d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Tom=C3=A1=C5=A1=20Kou=C5=99im?= Date: Thu, 4 Jun 2020 14:33:38 +0200 Subject: [PATCH 1/5] general graphs_generation.py --- config.py | 4 +++ graphs_generation.py | 25 +++++++++--------- ... with varying transition probabilities.pdf | Bin 540670 -> 540332 bytes ... with varying transition probabilities.tex | 2 +- 4 files changed, 18 insertions(+), 13 deletions(-) diff --git a/config.py b/config.py index 60f6e30..739ff97 100644 --- a/config.py +++ b/config.py @@ -26,3 +26,7 @@ BASE_GUESSES = [0.5, 0.8, 0.9, 0.7, 0.6, 0.2, 0.1, 0.4, 0.3] DECIMAL_PRECISION = 40 + +TICKS_SIZE=14 +LABEL_SIZE=18 +TITLE_SIZE=20 \ No newline at end of file diff --git a/graphs_generation.py b/graphs_generation.py index be87d15..d12d91c 100644 --- a/graphs_generation.py +++ b/graphs_generation.py @@ -6,7 +6,8 @@ from common import exp_p_t_array, var_p_t_array, log_time, create_logger, exp_s_t_array, exp_p_s_t_array, var_s_t_array, \ exp_x_t_array, var_x_t_array from config import MODEL_TYPES, REPETITIONS_OF_WALK_S, \ - C_LAMBDAS_TESTING, START_PROBABILITIES_TESTING, STEP_COUNTS_TESTING, C_LAMBDA_PAIRS_TESTING + C_LAMBDAS_TESTING, START_PROBABILITIES_TESTING, STEP_COUNTS_TESTING, C_LAMBDA_PAIRS_TESTING, TICKS_SIZE, LABEL_SIZE, \ + TITLE_SIZE from data_generation import generate_random_walks, list_walks2list_lists, generate_random_walk_from_rand_array @@ -113,17 +114,17 @@ def single_walk_simulation(model_type): else: two_lambda = False # TODO handle with dignity - max_y = 80 - min_y = -20 + max_y = 1 + min_y = 0 for p_index, starting_probability in enumerate(START_PROBABILITIES_TESTING): rand_numbers = np.random.uniform(size=step_count) plt.subplot(plt_rows, plt_columns, p_index + 1) - plt.title(r'$p_{0}=%.2f$' % starting_probability, fontsize=20) - plt.axis([1, step_count, min_y, max_y]) - plt.xlabel('steps', fontsize=18) - plt.xticks(fontsize=14) - plt.yticks(fontsize=14) + plt.title(r'$p_{0}=%.2f$' % starting_probability, fontsize=TITLE_SIZE) + plt.axis([0, step_count, min_y, max_y]) + plt.xlabel('steps', fontsize=LABEL_SIZE) + plt.xticks(fontsize=TICKS_SIZE) + plt.yticks(fontsize=TICKS_SIZE) for index, c_lambda in enumerate(C_LAMBDAS_TESTING): if two_lambda: c_lambdas = C_LAMBDA_PAIRS_TESTING[index] @@ -131,9 +132,9 @@ def single_walk_simulation(model_type): else: c_lambdas = [c_lambda] label = r'$\lambda=%.2f$' % c_lambda - development = generate_random_walk_from_rand_array(rand_numbers, model_type, starting_probability, - c_lambdas, step_count).development - plt.plot(development, styles[index], label=label) + data_to_plot = generate_random_walk_from_rand_array(rand_numbers, model_type, starting_probability, + c_lambdas, step_count).probabilities + plt.plot(data_to_plot, styles[index], label=label) plt.legend(loc='best', fontsize='xx-large', markerscale=3) fig = plt.gcf() fig.set_size_inches(18.5, 10.5) @@ -147,5 +148,5 @@ def single_walk_simulation(model_type): # main(simulated_property="probability") # main(simulated_property="step") # main(simulated_property="p_s") - single_walk_simulation("success_punished") + single_walk_simulation("success_punished_two_lambdas") log_time(start_time, logger) diff --git a/paper/presentation/A model of random walk with varying transition probabilities.pdf b/paper/presentation/A model of random walk with varying transition probabilities.pdf index cf460027956c374f05a4c0299b553db65a603406..c76b2f66e0c73860558a57693ffd44a077964fb0 100644 GIT binary patch delta 34750 zcmai-2e?($wYIZS_D0kwU;{*tU2N=C_F8LONDv#KS4E9cqgO7dXcPoXG*PxKHY_OD zEIWz{0UMxrKt-@%Zx~BryQoposMr!~;{VRw*Z9u!{5~;w26N3a=9puAqs)2!^Hawi z|L&Obt6XX7+{?D9j5wfwdF_XOICw>J*P+`UH|&-tu6XW|U(K68aLMyWT)E5D59bg5 zvB%>_TwIwp?$}%V_V0he+9OvljQIZLmE-2`(c{#mtNw7$X7}x}q}PcL4%w}E)aJjN zJ?5q1KYwY?`xjoi(=lsZedEp(2aUM)f-k%spLp_;Ev|U{qwgjUd;hj$m;Zj!q!;t! z)}H)}=Xal8S@ZAL?>c<%CAW6_tW?}@gAq$-AM)Y(r))Iko&kQZk#Ar1$z{EsS@Wdd 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zIbyV{rXp(FNe)S#K!j$lQ5{54G8Lw}V!5;I+6l@AjW8|#>yUQ+j+GK`&>pGvgeGU# z(X5(wNRd~F+YN2kha0Bt2aTCDX{!6x&ZvUE{D${KC!RUU{m9NIKOWTgM}z%fB);K6 zQFKu0zykqa!{HE$!}H$oAUrS%M-1)z|8Mf+zWfUE^QVrRGWDV Date: Thu, 4 Jun 2020 15:08:52 +0200 Subject: [PATCH 2/5] modifiable marker sizes --- config.py | 6 +++--- graphs_generation.py | 8 ++++---- 2 files changed, 7 insertions(+), 7 deletions(-) diff --git a/config.py b/config.py index 739ff97..48ac9aa 100644 --- a/config.py +++ b/config.py @@ -27,6 +27,6 @@ DECIMAL_PRECISION = 40 -TICKS_SIZE=14 -LABEL_SIZE=18 -TITLE_SIZE=20 \ No newline at end of file +TICKS_SIZE = 14 +LABEL_SIZE = 25 +TITLE_SIZE = 30 diff --git a/graphs_generation.py b/graphs_generation.py index d12d91c..d68e278 100644 --- a/graphs_generation.py +++ b/graphs_generation.py @@ -33,11 +33,11 @@ def main(simulated_property="probability"): model_max_y[model_index] for p_index, starting_probability in enumerate(START_PROBABILITIES_TESTING): plt.subplot(plt_rows, plt_columns, p_index + 1) - plt.title(r'$p_{0}=%.2f$' % starting_probability, fontsize=20) + plt.title(r'$p_{0}=%.2f$' % starting_probability, fontsize=TITLE_SIZE) plt.axis([1, step_count, min_y, max_y]) - plt.xlabel('steps', fontsize=18) - plt.xticks(fontsize=14) - plt.yticks(fontsize=14) + plt.xlabel('steps', fontsize=LABEL_SIZE) + plt.xticks(fontsize=TICKS_SIZE) + plt.yticks(fontsize=TICKS_SIZE) for index, c_lambda in enumerate(C_LAMBDAS_TESTING): if two_lambda: c_lambdas = C_LAMBDA_PAIRS_TESTING[index] From ac02f8181744418c736b65c71f07a0d5f5fbc361 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Tom=C3=A1=C5=A1=20Kou=C5=99im?= Date: Thu, 4 Jun 2020 18:26:00 +0200 Subject: [PATCH 3/5] presentation updated to suit online format --- ... with varying transition probabilities.pdf | Bin 540332 -> 597899 bytes ... with varying transition probabilities.tex | 74 ++++++++++-------- ...teps_type_success_punished_two_lambdas.pdf | Bin 0 -> 10213 bytes ...teps_type_success_punished_two_lambdas.pdf | Bin 0 -> 10561 bytes 4 files 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\includegraphics[width=1\textwidth]{../../simulations/probability_25_steps_type_success_punished_two_lambdas} + \end{frame} + \begin{frame}{Motivation} \begin{itemize} \item Failure of a machine @@ -72,27 +76,31 @@ \end{itemize} \end{frame} + \begin{frame}{Motivation - Random process with varying probability} + \includegraphics[width=1\textwidth]{../../simulations/probability_dots_25_steps_type_success_punished_two_lambdas} + \end{frame} + \begin{frame}{Random walk with varying probabilities} \begin{itemize} - \item Random walk with memory - \item Memory coefficient $\lambda\in(0,\,1)$ affecting the transition probabilities - \item First step of the walk $X_{1}$ depends on an initial transition probability $p_{0}$ - \item Further steps depend on a transition probability $p_{t}$ evolving as - \onslide<2->\begin{flalign*} - X_{t-1} & =1\rightarrow p_{t}=\lambda p_{t-1} & - X_{t-1} & =-1\rightarrow p_{t}=1-\lambda(1-p_{t-1}) & + \item<1-> Random walk with memory based the on standard Bernoulli random walk + \item<2-> Given starting probability $p_0$ + \item<3-> $X_t\in\{-1,1\}$ with $X_t \sim {\textrm{Bernoulli} }(p_{t-1})$ + \item<4-> Memory coefficient $\lambda\in(0,\,1)$ affecting the development of probabilities $p_{t}$ as + \onslide<4->\begin{flalign*} + X_{t} & =1\rightarrow p_{t}=\lambda p_{t-1} & + X_{t} & =-1\rightarrow p_{t}=1-\lambda(1-p_{t-1}) & \end{flalign*} \vspace{-5mm} \begin{itemize} - \item[-->]<3-> ``Success punished'' + \item[-->]<5-> ``Success punished'' \end{itemize} - \onslide<4->\begin{flalign*} - X_{t-1}&=1\rightarrow p_{t}=1-\lambda(1-p_{t-1})& - X_{t-1}&=-1\rightarrow p_{t}=\lambda p_{t-1}& + \onslide<6->\begin{flalign*} + X_{t}&=1\rightarrow p_{t}=1-\lambda(1-p_{t-1})& + X_{t}&=-1\rightarrow p_{t}=\lambda p_{t-1}& \end{flalign*} \vspace{-5mm} \begin{itemize} - \item[-->]<5-> ``Success rewarded'' + \item[-->]<6-> ``Success rewarded'' \end{itemize} \end{itemize} \end{frame} @@ -174,6 +182,7 @@ \end{frame} \begin{frame}{Success rewarding model} + \onslide<2-> \begin{flalign*} EX_{t} & =2p_{0}-1 & \end{flalign*} @@ -181,10 +190,12 @@ \begin{flalign*} Var\,X_{t} & =4p_{0}(1-p_{0}) & \end{flalign*} + \onslide<1-> \begin{flalign*} EP_{t} & =p_{0} & \end{flalign*} \vspace{-8mm} + \onslide<2-> \begin{flalign*} Var\,P_{t} & =(2\lambda-\lambda^{2})^{t}p_{0}^{2}+p_{0}(1-\lambda)^{2}\sum_{i=0}^{t-1}(2\lambda-\lambda^{2})^{i}-p_{0}^{2} & \end{flalign*} @@ -197,7 +208,7 @@ \end{flalign*} \end{frame} - \begin{frame}{Two-parameter model} + \begin{frame}{More complex models} \begin{itemize} \item Two $\lambda$ parameters each affecting one direction of the walk \item Again two variants -- success punishing and success rewarding @@ -217,6 +228,7 @@ \begin{itemize} \item[-->]<3-> ``Two-parameter success rewarding model'' \end{itemize} + \item<4-> $M$ steps, $\lambda(t)$, $n$-dimensional walk \end{itemize} \end{frame} @@ -226,9 +238,9 @@ \begin{frame}{Model fitting} \begin{enumerate} - \item Find $\overrightarrow{\lambda}$ with known $p_{0}$, model type - \item Find $p_{0}$ with known $\overrightarrow{\lambda}$, model type - \item Find $p_{0},\,\overrightarrow{\lambda}$ with known model type + \item Find $\lambda$ with known $p_{0}$, model type + \item Find $p_{0}$ with known $\lambda$, model type + \item Find $p_{0},\,\lambda$ with known model type \item Find model type without any prior knowledge \end{enumerate} \end{frame} @@ -239,7 +251,7 @@ \item Find $p_{0}$ with known $\overrightarrow{\lambda}$, model type \item Find $p_{0},\,\overrightarrow{\lambda}$ with known model type \begin{itemize} - \item Using maximal likelihood estimate \& numerical optimization + \item (1-3) maximal likelihood estimate \& numerical optimization \end{itemize} \item Find model type without any prior knowledge \end{enumerate} @@ -251,11 +263,11 @@ \item Find $p_{0}$ with known $\overrightarrow{\lambda}$, model type \item Find $p_{0},\,\overrightarrow{\lambda}$ with known model type \begin{itemize} - \item Using maximal likelihood estimate \& numerical optimization + \item (1-3) maximal likelihood estimate \& numerical optimization \end{itemize} \item Find model type without any prior knowledge \begin{itemize} - \item Using Akaike information criterion \& numerical optimization + \item (4) Akaike information criterion \& numerical optimization \end{itemize} \end{enumerate} \end{frame} @@ -266,10 +278,10 @@ \item Model trained on 2009--2018 men Grand Slam tournaments \item<2-> Model applied on 2019 US Open \begin{itemize} - \item<2-> Live betting against bookmaker - \item<2-> $0.52$ units total necessary bankroll - \item<2-> $2.24$ units total profit $\rightarrow$ $430\%$ ROI - \item<3-> Only 128 bets placed + \item<3-> Live betting against bookmaker + \item<4-> Bankroll: $0.52$ units + \item<5-> Profit: $2.24$ units $\rightarrow$ $430\%$ ROI + \item<6-> Only 128 bets placed \end{itemize} \end{itemize} \end{frame} @@ -278,8 +290,8 @@ \begin{itemize} \item A specific model of a random walk with memory \item Model properties derived - \item Application shows big future potential of the model \item Possible applications in a set of real life scenarios + \item Initial results show big potential of the model \end{itemize} \end{frame} diff --git a/simulations/probability_25_steps_type_success_punished_two_lambdas.pdf b/simulations/probability_25_steps_type_success_punished_two_lambdas.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f325c867ba93f8b656bd7e688876b63259e3e975 GIT binary patch literal 10213 zcmb_?2{=^W`?x|h$QIIi5fPbv##plxV=oG2>|-~^9wE^}NtP5!mMkr{7DOVlMMUW% zN{O;X8?Aoljui5IAJ6~!&-0u)_rCX>_q^MA-}m14h#P5W?Lf=o5aL&!Lj~msG=zdY zZCwzGiV)I>;^g21VF1JgLYf77IY3Bt3Z3HS=>#b&BOE;J;em4VCTIrGwN2?1x&wrp zouuXIL5Hxj*G3dN-GSx-;o(~Z(un41XX-$QEWtV&S^&R803AZ=x`Q>Uzp^b=dvX?>_`<0_6guUcO)_acCVA57OIl3b{AF^lFGw&k-L?_xZPt|JgRK8d=F% zy}gSSnfhoZ(5vamN*xukRMG4Tukz#Dkfh?eu0SJ0($GG|b6el!1XzY}8NQ`jS=R{_ zpiZvtkSXioRP52dnB7mm6yo-x&aWV^OWv;S3$L5Dqgf#Lxh)gdvKj}fppp=licinG 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z6bwk1;uDJ%LBb;R7AcMovxxRt1C!qu>tGmWNhK;??PoDKl&b&+1@{}KqKsB7sTQjH zKq^+sgk`mnqLKqd_akG*MaC50j40}oe;fb4u4$#FruUmCspbX!POw6hSOcbxz`)R$ z^S5)D81*JL!As4oE$s|(Smuwffhtn(k^y8PWwn)2pP2q3!W5Tpy%R;KR6Qn?W84(a zdak4e5KOy?t%S-%vHYtBv>gJBqEr)+`oC|2f3WhsF<4VxBvf;Pu{-oeNVph$_rn7 a<+s21;!97k8K2Oi>dAA@edr?}e)7NFV#d7y diff --git a/paper/presentation/A model of random walk with varying transition probabilities.tex b/paper/presentation/A model of random walk with varying transition probabilities.tex index 7044ead..ad385b2 100644 --- a/paper/presentation/A model of random walk with varying transition probabilities.tex +++ b/paper/presentation/A model of random walk with varying transition probabilities.tex @@ -12,8 +12,8 @@ \usecolortheme{beaver} -\title{A model of random walk with varying transition probabilities} -\institute[FNSPE CTU]{\inst{1} Faculty of Nuclear Sciences and Physical Engineering, CTU Prague \and +\title{A Model of a Random Walk with Varying Transition Probabilities} +\institute[Tomáš Kouřim (tom@skourim.com)]{\inst{1} Faculty of Nuclear Sciences and Physical Engineering, CTU Prague \and \inst{2} Institute of Information Theory and Automation, CAS CR Prague} \date{SMTDA 2020} \author[Tomáš~Kouřim]{Tomáš~Kouřim \inst{1} \and Petr Volf \inst{2}} @@ -33,6 +33,7 @@ % \item<3-> {\Large{}Model application} % \end{enumerate} % \end{frame} + \section{Motivation} \begin{frame}{Random walk} \begin{definition} @@ -80,6 +81,7 @@ \includegraphics[width=1\textwidth]{../../simulations/probability_dots_25_steps_type_success_punished_two_lambdas} \end{frame} + \section{Model description} \begin{frame}{Random walk with varying probabilities} \begin{itemize} \item<1-> Random walk with memory based the on standard Bernoulli random walk @@ -92,7 +94,7 @@ \end{flalign*} \vspace{-5mm} \begin{itemize} - \item[-->]<5-> ``Success punished'' + \item[-->]<5-> ``Success punishing'' \end{itemize} \onslide<6->\begin{flalign*} X_{t}&=1\rightarrow p_{t}=1-\lambda(1-p_{t-1})& @@ -100,7 +102,7 @@ \end{flalign*} \vspace{-5mm} \begin{itemize} - \item[-->]<6-> ``Success rewarded'' + \item[-->]<6-> ``Success rewarding'' \end{itemize} \end{itemize} \end{frame} @@ -210,7 +212,7 @@ \begin{frame}{More complex models} \begin{itemize} - \item Two $\lambda$ parameters each affecting one direction of the walk + \item Two memory coefficients $\lambda$ each affecting one direction of the walk \item Again two variants -- success punishing and success rewarding \onslide<2->\begin{flalign*} X_{t-1} & =1\rightarrow p_{t}=\lambda_{0} p_{t-1} & @@ -236,36 +238,37 @@ \includegraphics[width=1\textwidth]{../../simulations/single_walk_1000_steps_type_success_punished_two_lambdas} \end{frame} + \section{Model application} \begin{frame}{Model fitting} \begin{enumerate} \item Find $\lambda$ with known $p_{0}$, model type \item Find $p_{0}$ with known $\lambda$, model type \item Find $p_{0},\,\lambda$ with known model type - \item Find model type without any prior knowledge + \item Find model type and all parameters without any prior knowledge \end{enumerate} \end{frame} \begin{frame}{Model fitting} \begin{enumerate} - \item Find $\overrightarrow{\lambda}$ with known $p_{0}$, model type - \item Find $p_{0}$ with known $\overrightarrow{\lambda}$, model type - \item Find $p_{0},\,\overrightarrow{\lambda}$ with known model type + \item Find $\lambda$ with known $p_{0}$, model type + \item Find $p_{0}$ with known $\lambda$, model type + \item Find $p_{0},\,\lambda$ with known model type \begin{itemize} \item (1-3) maximal likelihood estimate \& numerical optimization \end{itemize} - \item Find model type without any prior knowledge + \item Find model type and all parameters without any prior knowledge \end{enumerate} \end{frame} \begin{frame}{Model fitting} \begin{enumerate} - \item Find $\overrightarrow{\lambda}$ with known $p_{0}$, model type - \item Find $p_{0}$ with known $\overrightarrow{\lambda}$, model type - \item Find $p_{0},\,\overrightarrow{\lambda}$ with known model type + \item Find $\lambda$ with known $p_{0}$, model type + \item Find $p_{0}$ with known $\lambda$, model type + \item Find $p_{0},\,\lambda$ with known model type \begin{itemize} \item (1-3) maximal likelihood estimate \& numerical optimization \end{itemize} - \item Find model type without any prior knowledge + \item Find model type and all parameters without any prior knowledge \begin{itemize} \item (4) Akaike information criterion \& numerical optimization \end{itemize} @@ -279,8 +282,8 @@ \item<2-> Model applied on 2019 US Open \begin{itemize} \item<3-> Live betting against bookmaker - \item<4-> Bankroll: $0.52$ units - \item<5-> Profit: $2.24$ units $\rightarrow$ $430\%$ ROI + \item<4-> Bankroll: $52$ units + \item<5-> Profit: $224$ units $\rightarrow$ $430\%$ ROI \item<6-> Only 128 bets placed \end{itemize} \end{itemize} From 6338c650941dccf2977050f4737226cd306f920e Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Tom=C3=A1=C5=A1=20Kou=C5=99im?= Date: Fri, 5 Jun 2020 17:47:08 +0200 Subject: [PATCH 5/5] labels added --- ...m walk with varying transition probabilities.tex | 13 +++---------- 1 file changed, 3 insertions(+), 10 deletions(-) diff --git a/paper/presentation/A model of random walk with varying transition probabilities.tex b/paper/presentation/A model of random walk with varying transition probabilities.tex index ad385b2..7956789 100644 --- a/paper/presentation/A model of random walk with varying transition probabilities.tex +++ b/paper/presentation/A model of random walk with varying transition probabilities.tex @@ -26,14 +26,7 @@ \begin{document} \maketitle -% \begin{frame}{Outline} -% \begin{enumerate} -% \item<1-> {\Large{}Motivation}\bigskip{} -% \item<2-> {\Large{}Model description}\bigskip{} -% \item<3-> {\Large{}Model application} -% \end{enumerate} -% \end{frame} - \section{Motivation} + \section{Motivation}\label{sec:motivation} \begin{frame}{Random walk} \begin{definition} @@ -81,7 +74,7 @@ \includegraphics[width=1\textwidth]{../../simulations/probability_dots_25_steps_type_success_punished_two_lambdas} \end{frame} - \section{Model description} + \section{Model description}\label{sec:model-description} \begin{frame}{Random walk with varying probabilities} \begin{itemize} \item<1-> Random walk with memory based the on standard Bernoulli random walk @@ -238,7 +231,7 @@ \includegraphics[width=1\textwidth]{../../simulations/single_walk_1000_steps_type_success_punished_two_lambdas} \end{frame} - \section{Model application} + \section{Model application}\label{sec:model-application} \begin{frame}{Model fitting} \begin{enumerate} \item Find $\lambda$ with known $p_{0}$, model type

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