Comparing Asymmetric models p2 asymmetric semantic search

case 2 | comparison of SBERT models for asymmetric semantic search on course data (for searching for docs that are relevant quickly

query for all 3 models is the same, QUERY: deciding whether a time series is stationary

## sentence-transformers/msmarco-bert-base-dot-v5

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  'doc_dir': 'TB-theory-and-methods-1992',
  'doc_name': 'OCR_3_Stationary Time Series_Time Series Theory and Methods_',
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  'doc_text': ', - 1 ) ( ( + 02 ) oz if h = 0, 0oz if h = + 1, if | hl > 1, 14 '
              '1. stationary time series and hence { x, } is stationary. in '
              'fact it can be shown that { x, } is strictly stationary ( see '
              'problem 1. 1 ). example 1. 3. 3. let sx if t is even, x, = ( y '
              '+ 1 if t is odd. where { y } is a stationary time series. '
              'although cov ( x, th, x, ) = yr ( h ), { x, } is not stationary '
              'for it does not have a constant mean. example 1. 3. 4 referring '
              'to example 1. 2. 3, let s be the random walk s = x + xz + + x, '
              'where x,, x2, are independent and identically distributed with '
              'mean zero and variance 02. for h > 0, cov ( sth, s ) = cov xi, '
              'ax ) cov xax ) 02 and thus s is not stationary. stationary '
              'processes play a crucial role in the analysis of time series of '
              'course many observed time series ( see section 1. 1 ) are '
              'decidedly nonstationary in appearance. frequently',
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 {'Rank': 2,
  'Search Score': 171.1249,
  'doc_dir': 'lecture-audio',
  'doc_name': 'SC_lecture_1_feb_21_v_2_c_transcription_4',
  'doc_relative_loc': 41.818,
  'doc_text': 'examples are stationary or not. so this is the question you ask '
              ': this is a time series that is not stationary because here, '
              "it's very imped. well, have to be careful. even more so, making "
              'a statement that this time series is not stationary is too '
              'bold. stationary is a property of a time series process of the '
              "random reveals here is only see data ; in fact, i don't know "
              'how the serious process is. the time series process which '
              "generated these data is either stationary, or it's not. but i "
              "don't know the process, and it's hard to make a statement about "
              'it. what i see is data is observations. and of course, if the '
              'data looks like this and it seems highly implausible that the '
              'underlying data generating process is stationary because here '
              'it seems that the means of this observation, so the is of that '
              'one is not identical with the most of this one. it also seems '
              'very unlikely that i could take a snip it out of this time '
              'series and shift it somewhere and exchange this snip and her '
              'with that one so that it would look very puzzling on this '
              'ground ; it seems very implausible that this is generated from '
              'a stationary process. so basically, here, we do',
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 {'Rank': 3,
  'Search Score': 170.6889,
  'doc_dir': 'practice-exams',
  'doc_name': 'OCR_e-2020-wi-problems_',
  'doc_relative_loc': 10.0,
  'doc_text': 'series process? a ) yes b ) no ; because the mean is not 0 no '
              'because there is a trend d ) more than one of the above answers '
              'is correct 3 200 400 600 800 1000 1200 time 3 u six _ ( 3 '
              'points ) is it reasonable to model the following time series '
              'with a stationary time series process? a ) yes ; under all '
              'circumstances b ) yes ; but only if the cyclic component is non '
              '- deterministic c ) yes ; but only if the cyclic component is '
              'deterministic 8 " 200 400 600 800 time 7 _ ( 3 points ) the r - '
              'functions acf ( ) and pack ( ) are used to compute and '
              'visualize the theoretical acf and pacf of an observed time '
              'series. true b ) false 8 ( 3 points ) time series xt can be '
              'decomposed as xt = mt + st + rt ; where it is the trend ; st '
              'the seasonal component, and rt the remainder term ; only if xt '
              'is a ) white noise a stationary time series 6 ) a non - '
              'stationary time series that can be made stationary taking '
              'differences at appropriate lags d ) none of the above answers '
              'is correct. nine _ ( 4 points ) suppose we are given a '
              'stationary time series xt and that we also consider y',
  'id_within_doc': 3}]

---------------------------------------------------------------------------------------------


## sentence-transformers/msmarco-distilbert-cos-v5


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  'doc_dir': 'TB-theory-and-methods-1992',
  'doc_name': 'OCR_3_Stationary Time Series_Time Series Theory and Methods_',
  'doc_relative_loc': 28.205,
  'doc_text': ', - 1 ) ( ( + 02 ) oz if h = 0, 0oz if h = + 1, if | hl > 1, 14 '
              '1. stationary time series and hence { x, } is stationary. in '
              'fact it can be shown that { x, } is strictly stationary ( see '
              'problem 1. 1 ). example 1. 3. 3. let sx if t is even, x, = ( y '
              '+ 1 if t is odd. where { y } is a stationary time series. '
              'although cov ( x, th, x, ) = yr ( h ), { x, } is not stationary '
              'for it does not have a constant mean. example 1. 3. 4 referring '
              'to example 1. 2. 3, let s be the random walk s = x + xz + + x, '
              'where x,, x2, are independent and identically distributed with '
              'mean zero and variance 02. for h > 0, cov ( sth, s ) = cov xi, '
              'ax ) cov xax ) 02 and thus s is not stationary. stationary '
              'processes play a crucial role in the analysis of time series of '
              'course many observed time series ( see section 1. 1 ) are '
              'decidedly nonstationary in appearance. frequently',
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  'doc_dir': 'lecture-audio',
  'doc_name': 'SC_lecture_1_feb_21_v_2_c_transcription_4',
  'doc_relative_loc': 43.636,
  'doc_text': 'that this is generated from a stationary process. so basically, '
              "here, we don't have stationary. hence, the variant rule is as "
              "it's written on that slide variant has to be constant, and the "
              'conjecture of that is that these time series are very unlikely '
              'to be stationary, so be careful about the wording. so the time '
              '- serious process underlying these data is unlikely to be '
              "stationary's the correct wording. so usually, just say, well, "
              "the series is not stationary, but it's a bit of a bold "
              'statement. but this is what i usually say, and you must '
              'understand what it means exactly, so well, time will be up in a '
              "few seconds. this one is here. stationary or not, it's a good "
              'question. can we move around snippets or not? if you look at '
              'this feature, for example, in the first place, you may say no, '
              "it's so regular, so if we just shift that a little bit, then it "
              'does not look good anymore. but then, if you look at that, it '
              'seems to be that nature. so, we will consider this as great '
              'stationery. okay, so we have to stop here yet. maybe just a '
              'last remark : what we',
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  'doc_name': 'SC_lecture_2_feb_28_v_2_c_transcription_5',
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  'doc_text': 'because these are simulated data. so here i know the time semi '
              '- time series line for the data generation. so i can make a '
              'strict statement about whether the time series process is '
              "stationary. however, you only see the data, so you're obviously "
              'in a more difficult position, so you have to make up your mind '
              'with the usual tools. he forgot to prepare many questions, but '
              'maybe, we can clarify quickly by just answering. what do you '
              'think is the torso in the usual form, stationary or not, in '
              'this first example? or maybe we have to vote for man, who is '
              "for stationary in this one. so and maybe i can add i don't try "
              'to trick you. i mean, i could always produce something that '
              "looks stationary. and then i could say, well, it's not because "
              'i added a tiny epsilon that makes it not detectable stationery. '
              "but i don't try to trick you. well, it's fairer. so stationary. "
              "who's for stationary at this is the majority, and it's true. "
              'this arises from a stationary process. yes, so what about this '
              "one? so if you have to decide who is stationary, it's very few, "
              'only you, but understandably, this is',
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---------------------------------------------------------------------------------------------


## sentence-transformers/msmarco-distilbert-base-tas-b


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  'doc_dir': 'TB-time-seriesR-cowpertwait',
  'doc_name': 'OCR_9_Stationary Models_intro time series in R - cowperwait_',
  'doc_relative_loc': 3.333,
  'doc_text': 'in this chapter _ the term stationary was discussed in previous '
              'chapters ; we now give a more rigorous definition. 6. 2 '
              'strictly stationary series a time series model { tt } is '
              'strictly stationary if the joint statistical distribution of '
              'tt1 itn is the same as the joint distribution of tt1 + m ; ttn '
              '+ m for all t1, tn and m, s0 that the distribution is unchanged '
              'after an arbitrary time shift _ note that strict stationarity '
              'implies that the mean and variance are constant in time and '
              'that the autocovariance cov ( xt, x $ only depends on lag k = '
              'it s | and can be written ~ ( k ). if a series is not strictly '
              'stationary but the mean and variance are constant in time and '
              'the autocovariance only ps. p cowpertwait and a. v. metcalfe, '
              'introductory time series with r, use r, doi 10. 1007 / 978 - 0 '
              '- 387 - 88698 - 5 _ 6, springer science + business media, llc '
              "2009 121 122 stationary models depends on the lag ;'then the "
              'series is called second - order stationary : we focus on the '
              'second - order properties in this chapter ; but the stochastic '
              'processes discussed are',
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  'doc_dir': 'TB-theory-and-methods-1992',
  'doc_name': 'OCR_3_Stationary Time Series_Time Series Theory and Methods_',
  'doc_relative_loc': 28.205,
  'doc_text': ', - 1 ) ( ( + 02 ) oz if h = 0, 0oz if h = + 1, if | hl > 1, 14 '
              '1. stationary time series and hence { x, } is stationary. in '
              'fact it can be shown that { x, } is strictly stationary ( see '
              'problem 1. 1 ). example 1. 3. 3. let sx if t is even, x, = ( y '
              '+ 1 if t is odd. where { y } is a stationary time series. '
              'although cov ( x, th, x, ) = yr ( h ), { x, } is not stationary '
              'for it does not have a constant mean. example 1. 3. 4 referring '
              'to example 1. 2. 3, let s be the random walk s = x + xz + + x, '
              'where x,, x2, are independent and identically distributed with '
              'mean zero and variance 02. for h > 0, cov ( sth, s ) = cov xi, '
              'ax ) cov xax ) 02 and thus s is not stationary. stationary '
              'processes play a crucial role in the analysis of time series of '
              'course many observed time series ( see section 1. 1 ) are '
              'decidedly nonstationary in appearance. frequently',
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  'doc_dir': 'lecture-audio',
  'doc_name': 'SC_lecture_3_mar_7_v_2_c_transcription_6',
  'doc_relative_loc': 35.294,
  'doc_text': 'in this first part might be slightly lower than, for example, '
              'in this part. so here, the decision is not clear. certainly, '
              'this series here, as it appears, is not very far from what you '
              'could produce from a stationary time series process. so here '
              'for this series. not a very clear reject of that hypothesis '
              "that it's generated from a stationary process. still, and that "
              "is by experience to some extent. by well, let's say theoretical "
              'motivation that there are time series processes which work '
              'pretty well if you declare this as being none stationary and '
              "requiring another difference. i'll summarize it, but let's just "
              'look at the result. so we say, well, this is cannon stationery, '
              'so it still has some trend in it, and we just do a different '
              "step at it one. so this is what we do again. i mean, it's very "
              'useful to write that using these operations with the makeshift '
              'operator. so why is it the seasonally different series, and '
              'then we just make differences at onto one, lack one again to '
              'remove that potential trend? this is the full equation, and '
              'this is the series we obtain. you certainly have a lot more '
              'stationary than the one in i think you can not object',
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---------------------------------------------------------------------------------------------


## sentence-transformers/multi-qa-mpnet-base-dot-v1

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  'doc_name': 'SC_lecture_2_feb_28_v_2_c_transcription_5',
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  'doc_text': 'with the hypotheses, the question arises whether there are any '
              'formal tests for stationary. and while some tests exist, so the '
              'script has some hints and does not have them on the slides, '
              'there are in some kind practically worthless, and the reason '
              'for that is that a particular test for stationary typically '
              'only addresses a very particular violation of the stationary '
              'points. so there is nothing like a global test that would work '
              'in every situation. but mostly, these tests are such that they '
              'are very specific for certain kinds of stationary violations, '
              'and they have little to no power for other violations. so the '
              'only place for those formal tests is if you have some specific '
              'potential violation of the stationary assumption. you know that '
              'the tests you will be using an address that issue, and you '
              'could get an answer. the deviation you observe in the data is '
              'important enough to call it a significant violation of '
              "stationary, but globally they don't tend to work. and you get "
              'far further with visual analysis based on the time series plot '
              'and kind of good feeling witches associated with it, then how '
              'does it work? i suggest we take time - series blocks and decide '
              "based on them. and the rule is that's the one in the yellow "
              'box, and i think this helps pretty far. so we must',
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  'doc_dir': 'course-slides',
  'doc_name': 'OCR_ATS_Slides_v220216__1',
  'doc_relative_loc': 50.0,
  'doc_text': 'non - stationarity in a stationary series, one can move any '
              'random snippet of the series to any other location of choice. '
              'if that does not seem right, it is unlikely that the underlying '
              'process is stationary. particular violations of stationarity : '
              'trend, i. e. non - constant expected value seasonality, i. e. '
              'deterministic, periodical oscillations, non - constant '
              'variation, i. e. multiplicative error non - constant dependency '
              'structure remark : some periodical oscillations, as in the lynx '
              'data, are stochastic and originate from a stationary process. '
              'however, the boundary between the two is fuzzy. 24 mathematical '
              'concepts strategies for detecting non - stationarity 1 ) time '
              'series plot not being able to move any arbitrary snippet non - '
              'constant expectation ( trendy seasonal effect ) changes in the '
              'dependency structure non - constant variation 2 ) correlogram ( '
              'presented later _ _ ) non - constant expected value ( trendy '
              'seasonal effect ) changes in the dependency structure a ( '
              'sometimes ) useful trick, especially when working with the '
              'correlogram ; is to split up the series in two or more parts, '
              'and producing plots for each of the pieces separately. 25 '
              'mathematical concepts example : simulated time series 1 '
              'simulated time series',
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  'doc_dir': 'TB-forecasting-principles',
  'doc_name': 'OCR_Ch-9-ARIMA models-FPP_',
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  'doc_text': ') annual number of strikes in the us ; ( d ) monthly sales of '
              'new onefamily houses sold in the us ; ( e ) annual price of a '
              'dozen eggs in the us ( constant dollars ) ; ( f ) monthly total '
              'of pigs slaughtered in victoria, australia ; ( g ) annual total '
              'of lynx trapped in the mckenzie river district of north - west '
              'canada ; ( h ) monthly australian beer production ; ( i ) '
              'monthly australian electricity production : consider the nine '
              'series plotted in figure 8. 1. which of these do you think are '
              'stationary? obvious seasonality rules out series ( d ), ( h ) '
              'and ( i ). trends and changing levels rules out series ( a ), ( '
              'c ), ( e ), ( f ) and ( i ). increasing variance also rules out '
              '( i ). that leaves only ( b ) and ( g ) as stationary series. '
              'at first glance, the strong cycles in series ( g ) might appear '
              'to make it nonstationary. but these cycles are aperiodic they '
              'are caused when the lynx population becomes too large for the '
              'available feed, so that they stop breeding ww and the '
              'population falls to low numbers, then the regeneration of their '
              'food sources allows the population to grow again, and s0 on.',
  'id_within_doc': 2}]


----------------------------